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Integer factorization (2,983 words) [view diff] no match in snippet view article find links to article

in computer science: Can integer factorization be solved in polynomial time on a classical computer? (more unsolved problems in computer science) In

In theoretical computer science, a circuit is a model of computation in which input values proceed through a sequence of gates, each of which computes

be defined for all integers k {\displaystyle k} , and the discrete logarithm log b ⁡ ( a ) {\displaystyle \log _{b}(a)} is an integer k {\displaystyle k}

parameters. Unlike argument in usual mathematical usage, the argument in computer science is the actual input expression passed/supplied to a function, procedure

In number theory, an evil number is a non-negative integer that has an even number of 1s in its binary expansion. These numbers give the positions of

complexity theory, and more specifically in the analysis of algorithms with integer data, the transdichotomous model is a variation of the random-access machine

32-bit integer. Thus the 32-bit integer Integer and 32-bit floating-point Float objects can simply use the value directly, whereas the 64-bit integer Long

In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same

integer that has an odd number of 1s in its binary expansion. Nonnegative integers that are not odious are called evil numbers. In computer science,

In theoretical computer science, a computational problem is one that asks for a solution in terms of an algorithm. For example, the problem of factoring

1983 32 4 64 8, 16 8, 16 1 2× integer No Partial Color key TI-99/4 & 4A TMS9918 1979 32 4 64 8, 16 8, 16 1 2× integer No Partial Color key Gameduino

Stefan (1983-01-01). "Upper bounds for sorting integers on random access machines". Theoretical Computer Science. 28 (3): 263–276. doi:10.1016/0304-3975(83)90023-3

In mathematics and computer science, the sorting numbers are a sequence of numbers introduced in 1950 by Hugo Steinhaus for the analysis of comparison

NP-Completeness. W.H. Freeman. ISBN 978-0-7167-1045-5. A6: MP1: INTEGER PROGRAMMING, pg.245. (computer science, complexity theory) Gärtner, Bernd; Matoušek, Jiří (2006)

In computer science, object composition and object aggregation are closely related ways to combine objects or data types into more complex ones. In conversation

and Discrete Optimizer) is a software package for linear programming, integer programming, nonlinear programming, stochastic programming and global optimization

is a software package for the solution of linear, mixed-integer linear, quadratic, mixed-integer quadratic, quadratically constrained, conic and convex

In mathematics and computer science, the Wedderburn–Etherington numbers are an integer sequence named after Ivor Malcolm Haddon Etherington and Joseph

In computer science, a hash table is a data structure that implements an associative array, also called a dictionary or simply map; an associative array

/ˈaɪdəm-/) is the property of certain operations in mathematics and computer science whereby they can be applied multiple times without changing the result

computer science, integer sorting is the algorithmic problem of sorting a collection of data values by integer keys. Algorithms designed for integer sorting

Hewlett-Packard calculators operated bit-serially. Assuming N is an arbitrary integer number, N serial processors will often take less FPGA area and have a higher

affected section of code. For example: The result of a factorial is always an integer and greater than or equal to 1. So a program that calculates the factorial

in computer science: ⁠ NP   = ?   co-NP {\displaystyle {\textsf {NP}}\ {\overset {?}{=}}\ {\textsf {co-NP}}} ⁠ (more unsolved problems in computer science)

In computer science, an array is a data structure consisting of a collection of elements (values or variables), of same memory size, each identified by

Informationstechnik Berlin) is a research institute for applied mathematics and computer science on the campus of Freie Universität Berlin in Dahlem, Berlin, Germany

In mathematics and computer science, truncation is limiting the number of digits right of the decimal point. Truncation of positive real numbers can be

visible integers; while file descriptors and sockets (which are often implemented as a form of file descriptor) are represented as integers, they are

an integer greater than or equal to zero. So an implementation of the factorial function would have a precondition that its parameter be an integer and

(AP) Computer Science A (also known as AP CompSci, AP CompSci A, AP CSA, AP Computer Science Applications, or AP Java) is an AP Computer Science course

Presburger's Article on Integer Arithmetic: Remarks and Translation (PDF) (Technical Report). Vol. TR84-639. Ithaca/NY: Dept. of Computer Science, Cornell University

Unsolved problem in computer science: If the solution to a problem is easy to check for correctness, must the problem be easy to solve? (more unsolved

In mathematics and computer science, computational number theory, also known as algorithmic number theory, is the study of computational methods for investigating

In computer science, a graph is an abstract data type that is meant to implement the undirected graph and directed graph concepts from the field of graph

are dyadic rationals, but 1/3 is not. These numbers are important in computer science because they are the only ones with finite binary representations.

In computer science, a lock or mutex (from mutual exclusion) is a synchronization primitive that prevents state from being modified or accessed by multiple

ArrayList(); v.add("test"); // A String that cannot be cast to an Integer final Integer i = (Integer) v.get(0); // Run time error Although the code is compiled

optimization is a branch of optimization in applied mathematics and computer science. As opposed to continuous optimization, some or all of the variables

these examples, or infinite, such as the sequence of all even positive integers (2, 4, 6, ...). The position of an element in a sequence is its rank or

Gusfield is an American computer scientist, Distinguished Professor of Computer Science at the University of California, Davis. Gusfield is known for his research

In mathematical optimization and computer science, a feasible region, feasible set, or solution space is the set of all possible points (sets of values

datatype of integer. type PersonRecord = record lastName : array [ 1 .. 20 ] of Char; firstName : array [ 1 .. 20 ] of Char; age : Integer end; In Pascal

that evaluates to integer constant. A default label consists of the keyword default. Case labels are used to associate an integer value with a statement

Stooge sort the initial 2/3 of the list again It is important to get the integer sort size used in the recursive calls by rounding the 2/3 upwards, e.g

group of enthusiasts at the Institute of Mathematics, Mechanics, and Computer Science in Rostov-on-Don, Russia. In 2003, a predecessor of the modern PascalABC

In mathematics, engineering, computer science and economics, an optimization problem is the problem of finding the best solution from all feasible solutions

theory, software engineering, VLSI, applied mathematics and theoretical computer science. Basic applications of combinatorial optimization include, but are

In computer science, a generator is a routine that can be used to control the iteration behaviour of a loop. All generators are also iterators. A generator

In computer science, algebraic semantics is a form of axiomatic semantics based on algebraic laws for describing and reasoning about program specifications

Index, the dataset maintained by search engine indexing Array index, an integer pointer into an array data structure BitTorrent index, a list of .torrent

Journal of Integer Sequences is a peer-reviewed open-access academic journal in mathematics, specializing in research papers about integer sequences.

and computer science. Euclidean division is based on the following result, which is sometimes called Euclid's division lemma. Given two integers a and

modulo a fixed integer. ACC0 corresponds to computation in any solvable monoid. The class is very well studied in theoretical computer science because of

Michael Lawrence Fredman is an emeritus professor at the Computer Science Department at Rutgers University, United States. He earned his Ph.D. from Stanford

Unsolved problem in computer science: Is there an X + Y {\displaystyle X+Y} sorting algorithm faster than O ( n 2 log ⁡ n ) {\displaystyle O(n^{2}\log

In theoretical computer science and mathematics, computational complexity theory focuses on classifying computational problems according to their resource

commutative algebra, algebraic geometry, statistics, and computer science. The set of integer points, or, more generally, the set of points of an affine

disciplines involving formal languages, including mathematical logic and computer science, a variable may be said to be either free or bound. Some older books

In computer science, counting sort is an algorithm for sorting a collection of objects according to keys that are small positive integers; that is, it

In computer science, and in particular functional programming, a hylomorphism is a recursive function, corresponding to the composition of an anamorphism

main(String[] args) { Set s = new TreeSet<Integer>(); Set<String> ss = s; // unchecked warning s.add(new Integer(42)); // another unchecked warning Iterator<String>

Occasionally "human-readable" is used to describe ways of encoding an arbitrary integer into a long series of English words. Compared to decimal or other compact

problem in computer science: P   = ?   N P {\displaystyle {\mathsf {P\ {\overset {?}{=}}\ NP}}} (more unsolved problems in computer science) In computational

pair ( U , S ) {\displaystyle ({\mathcal {U}},{\mathcal {S}})} and an integer t {\displaystyle t} ; the question is whether there is a set packing of

In computer science and mathematical logic, satisfiability modulo theories (SMT) is the problem of determining whether a mathematical formula is satisfiable

early 1990s established that monads could bring seemingly disparate computer-science problems under a unified, functional model. Category theory also provides

In computer science, manifest typing is explicit identification by the software programmer of the type of each variable being declared. For example: if

Unsolved problem in computer science: Do one-way functions exist? (more unsolved problems in computer science) In computer science, a one-way function

In mathematics and computer science, a canonical, normal, or standard form of a mathematical object is a standard way of presenting that object as a mathematical

In computer science, a type signature or type annotation defines the inputs and outputs of a function, subroutine or method.[citation needed] A type signature

In theoretical computer science, and specifically computational complexity theory and circuit complexity, TC0 (Threshold Circuit) is the first class in

finding integer relations among real numbers. Preliminary version: STACS 1986 (Symposium Theoret. Aspects Computer Science) Lecture Notes Computer Science 210

multiplied together Integer factorization, splitting a whole number into the product of smaller whole numbers Decomposition (computer science) A rule in resolution

exponentiation is exponentiation performed over a modulus. It is useful in computer science, especially in the field of public-key cryptography, where it is used

The cover tree is a type of data structure in computer science that is specifically designed to facilitate the speed-up of a nearest neighbor search. It

compareTo(T other); } public class Integer implements Comparable<Integer> { @Override public int compareTo(Integer other) { // ... } } public class String

a tree data structure which implements an associative array with m-bit integer keys. It was invented by a team led by Dutch computer scientist Peter van

particular subject. Many algorithms in the book depend on two's complement integer numbers. The subject matter of the second edition of the book includes

mathematical (often geometric) flavor that arise in Computer Science. He has worked on algorithms for integer programming and the geometry of numbers, random

In computer science, coalescing is a part of memory management in which two adjacent free blocks of computer memory are merged. When a program no longer

in computer science Partition problem, in number theory and computer science Integer partition, a way to write an integer as a sum of other integers Multiplicative

Alternative names are switching function, used especially in older computer science literature, and truth function (or logical function), used in logic

In mathematics and computer science, a recursive definition, or inductive definition, is used to define the elements in a set in terms of other elements

Shor's algorithm is a quantum algorithm for finding the prime factors of an integer. It was developed in 1994 by the American mathematician Peter Shor. It

remain limited. For many years, the fields of quantum mechanics and computer science formed distinct academic communities. Modern quantum theory developed

algorithm. This table lists the complexity of mathematical operations on integers. On stronger computational models, specifically a pointer machine and consequently

February 14, 2012. Retrieved November 10, 2008. A team of UT Dallas computer science students and their faculty adviser have improved upon a longstanding

In computer science and mathematical optimization, a metaheuristic is a higher-level procedure or heuristic designed to find, generate, tune, or select

theory and computer science became known. As part of his work in this area, Euler published a table of binary logarithms of the integers from 1 to 8

continuous functions). Objects studied in discrete mathematics include integers, graphs, and statements in logic. By contrast, discrete mathematics excludes

memory. The limit is created by the 32-bit integer limit (2,147,483,647), which is the largest possible integer that can be represented by 32 binary digits

interface that draws windows and/or their borders Function composition (computer science), an act or mechanism to combine simple functions to build more complicated

of the following in similar ways: empty strings, null references, the integer 0, the floating point number 0, the Boolean value false, the ASCII character

variable holding Integer value looks like this: private static final ThreadLocal<Integer> myThreadLocalInteger = new ThreadLocal<Integer>(); At least for

In combinatorics and computer science, covering problems are computational problems that ask whether a certain combinatorial structure 'covers' another

of Computer Science at the University of Illinois at Chicago. Before this, he was a visiting professor in the department of mathematics and computer science

L=F(K),\ M=F\circ F(K)=F^{2}(K).} Iterated functions are studied in computer science, fractals, dynamical systems, mathematics and renormalization group

second-order arithmetic. Kruskal's tree theorem, which has applications in computer science, is also undecidable from the Peano axioms but provable in set theory

a Bivariate Integer Equation; Factoring with High Bits Known". Advances in Cryptology — EUROCRYPT '96. Lecture Notes in Computer Science. Vol. 1070. pp

In computer science, Fhourstones is an integer benchmark that efficiently solves positions in the game of Connect-4. It was written by John Tromp in 1996-2008

In computer science, ACID (atomicity, consistency, isolation, durability) is a set of properties of database transactions intended to guarantee data validity

digit in a number system represents an integer. For example, in decimal the digit "1" represents the integer one, and in the hexadecimal system, the

In computer science, a scale factor is a number used as a multiplier to represent a number on a different scale, functioning similarly to an exponent in

combinatorics and analysis of algorithms, in the fields of theoretical computer science. This prize is named in memory of Philippe Flajolet. The Flajolet Lecture

In computer science, the AF-heap is a type of priority queue for integer data, an extension of the fusion tree using an atomic heap proposed by M. L.

architecture, these numbers have been called the harmonic whole numbers. In computer science, regular numbers are often called Hamming numbers, after Richard Hamming

In computer science, interning is re-using objects of equal value on-demand instead of creating new objects. This creational pattern is frequently used

programming languages. Scheme was created during the 1970s at the MIT Computer Science and Artificial Intelligence Laboratory (MIT CSAIL) and released by

satisfiability problem (SAT), satisfiability modulo theories (SMT), mixed integer programming (MIP) and answer set programming (ASP) are all fields of research

Theoretical computer science is a subfield of computer science and mathematics that focuses on the abstract and mathematical foundations of computation

In mathematics and computer science, a higher-order function (HOF) is a function that does at least one of the following: takes one or more functions as

fields of mathematical programming. The Integer Programming and Combinatorial Optimization (IPCO) conference, in integer programming, is held in those years

MY_CLASS and refer to it by: class MY_CLASS feature -- Access foo: INTEGER my_function: INTEGER do Result := foo end end Line #10 (above) has the implied reference

from number theory Quadratic residue, an integer that is a square modulo n Quadratic sieve, a modern integer factorization algorithm Quadratic convergence

published in The Bulletin of the European Association for Theoretical Computer Science. Both digital and analog hardware implementations of bead sort can

one-fourth of the integer precision used by a CDC 6600 supercomputer to disprove it two decades earlier via a brute force search. In computer science, modular

all strings. Many BASIC dialects use other sigils (like "%") to denote integers and floating-point numbers and their precision, and sometimes other types

In computer science, a fusion tree is a type of tree data structure that implements an associative array on w-bit integers on a finite universe, where

agreement with a symmetric encryption scheme. They are also used in several integer factorization algorithms that have applications in cryptography, such as

agreement with a symmetric encryption scheme. They are also used in several integer factorization algorithms that have applications in cryptography, such as

In computer science, a suffix array is a sorted array of all suffixes of a string. It is a data structure used in, among others, full-text indices, data-compression

efficiently as any other, no matter how many elements may be in the set. In computer science it is typically contrasted to sequential access which requires data

In computer science, pattern matching is the act of checking a given sequence of tokens for the presence of the constituents of some pattern. In contrast

binary operation and an identity element. For example, the nonnegative integers with addition form a monoid, the identity element being 0. Monoids are

In computer science, a lexical grammar or lexical structure is a formal grammar defining the syntax of tokens. The program is written using characters

to belong to L/poly, there must exist an advice function f that maps an integer n to a string of length polynomial in n, and a Turing machine M with two

a specific 14-digit (or 47-bit) integer, namely 79685186856218, and n is a specific 616-digit (or 2048-bit) integer that is the product of two large

In mathematics and computer science, Recamán's sequence is a well known sequence defined by a recurrence relation. Because its elements are related to

figure. The knapsack problem is interesting from the perspective of computer science for many reasons: The decision problem form of the knapsack problem

instances of these character sequences are termed lexemes). For example, an integer lexeme may contain any sequence of numerical digit characters. In many

group of Seif Haridi and Peter Van Roy at the Swedish Institute of Computer Science. Since 1999, Oz has been continually developed by an international

In computer science, a readers–writer (single-writer lock, a multi-reader lock, a push lock, or an MRSW lock) is a synchronization primitive that solves

In computer science, the block Lanczos algorithm is an algorithm for finding the nullspace of a matrix over a finite field, using only multiplication of

progressions. H. W. Lenstra Jr. for using the geometry of numbers to solve integer programs with few variables in time polynomial in the number of constraints

In computer science, a sorting algorithm is an algorithm that puts elements of a list into an order. The most frequently used orders are numerical order

mutable in the in out and out modes. procedure Do_it(a: in Integer; b: in out Integer; c: out Integer) is begin -- a is immutable b:= b + a; c:= a; end Do_it;

software design. Assume that two threads each increment the value of a global integer variable by 1. Ideally, the following sequence of operations would take

DEISA Benchmark Suite – scientific HPC applications benchmark Dhrystone – integer arithmetic performance, often reported in DMIPS (Dhrystone millions of

Computability, Complexity, and Languages: Fundamentals of Theoretical Computer Science, Computer Science and Scientific Computing (2nd ed.), Academic Press, p. 117

operations: For example, one doesn't sum characters or manipulate and process an integer array the same way as an image object. Neither does one process text as

SheetExists(sheetName As String) As Boolean Dim sheetCount As Integer Dim t As Integer SheetExists = False sheetCount = ActiveWorkbook.Sheets.Count For

language is a regular language for which there is an integer n such that for all words x, y, z and integers m ≥ n we have xymz in L if and only if xynz in L

composite integer n {\displaystyle n} , and in particular one which is the product of two large primes n = p ⋅ q {\displaystyle n=p\cdot q} , the integer factorization

number of the form 3n where n is an integer, that is, the result of exponentiation with number three as the base and integer n as the exponent. The powers of

branches of mathematics (graph theory) and computer science. Let S be a set of q elements and d a positive integer. The Hamming graph H(d,q) has vertex set

In computer science, the sign bit is a bit in a signed number representation that indicates the sign of a number. Although only signed numeric data types

members. Integer powers of 2 are important in computer science. The positive integer powers 2n give the number of possible values for an n-bit integer binary

and #Compare. Note that doing equality checks via a generic Compare with integer result is not only confusing for the programmer but is often a significantly

{\displaystyle x} is the excess beyond that number's integer part. The latter is defined as the largest integer not greater than x, called floor of x or ⌊ x ⌋

Specifically, consider bases b1 and b2 such that they are not powers of the same integer. Cobham's theorem states that S written in bases b1 and b2 is recognised

In computer science, extended Backus–Naur form (EBNF) is a family of metasyntax notations, any of which can be used to express a context-free grammar.

has to be called stand-alone, like DoSomething Function GiveMeFive() as Integer GiveMeFive= 5 End Function This returns the value 5, and a call can be

In number theory, two integers a and b are coprime, relatively prime or mutually prime if the only positive integer that is a divisor of both of them

In computer science, a recursive descent parser is a kind of top-down parser built from a set of mutually recursive procedures (or a non-recursive equivalent)

theory, a positive integer k is said to be an Erdős–Woods number if it has the following property: there exists a positive integer a such that in the

article is a list of notable unsolved problems in computer science. A problem in computer science is considered unsolved when no solution is known or

bounds, integer overflow and null dereferences. The techniques used in extended static checking come from various fields of computer science, including

In computer science and logic, a dependent type is a type whose definition depends on a value. It is an overlapping feature of type theory and type systems

computer science, a k-regular sequence is a sequence satisfying linear recurrence equations that reflect the base-k representations of the integers.

executes an empty body). All fields are left at their initial value of 0 (integer types), 0.0 (floating-point types), false (boolean type), or null (reference

is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855)

executes an empty body). All fields are left at their initial value of 0 (integer types), 0.0 (floating-point types), false (boolean type), or null (reference

is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. German mathematician Carl Friedrich Gauss (1777–1855)

In computer science, a type punning is any programming technique that subverts or circumvents the type system of a programming language in order to achieve

The set cover problem is a classical question in combinatorics, computer science, operations research, and complexity theory. Given a set of elements {1

tuple. An n-tuple is a tuple of n elements, where n is a non-negative integer. There is only one 0-tuple, called the empty tuple. A 1-tuple and a 2-tuple

paths Boolean circuit, a mathematical model for digital logic circuits Integer circuit, a mathematical object of computational complexity Circuit complexity

(2019). "Integer Programming and Incidence Treedepth". Integer Programming and Combinatorial Optimization (PDF). Lecture Notes in Computer Science. Vol. 11480

Fibonacci Quarterly (7): 525–32 "Marks for the da Vinci Code: B–", Maths, Computer Science For Fun: CS4FN Scott, T.C.; Marketos, P. (March 2014), On the Origin

is homeomorphic to a closed disk. The genus of a graph is the minimal integer n {\displaystyle n} such that the graph can be embedded in a surface of

encoded integer) that the CPU can process in one operation, which is commonly called word size, bit width, data path width, integer precision, or integer size

oriented as a "landscape". The aspect ratio is most often expressed as two integer numbers separated by a colon (x:y), less commonly as a simple or decimal

algorithms rely on the difficulty of one of three mathematical problems: the integer factorization problem, the discrete logarithm problem or the elliptic-curve

of integers using class groups. Prior to ANTS X, the refereed Proceedings of ANTS were published in the Springer Lecture Notes in Computer Science (LNCS)

Finite fields are fundamental in a number of areas of mathematics and computer science, including number theory, algebraic geometry, Galois theory, finite

function whose security, like that of RSA, is related to the difficulty of integer factorization. The Rabin trapdoor function has the advantage that inverting

In mathematics and computer science, a primality certificate or primality proof is a succinct, formal proof that a number is prime. Primality certificates

In mathematics, a real number is said to be simply normal in an integer base b if its infinite sequence of digits is distributed uniformly in the sense

individual objects (via EQL). Methods specialized on Common Lisp types (symbol, integer, ...). Methods specialized on def-struct types. Class slots. Howard Cannon

given length, meaning that for every positive integer k there are an integer a and a non-zero integer c such that { a , a + c , a + 2 c , … , a + k c

Dwork showed that a certain average-case lattice problem, known as short integer solutions (SIS), is at least as hard to solve as a worst-case lattice problem

In number theory, an n-smooth (or n-friable) number is an integer whose prime factors are all less than or equal to n. For example, a 7-smooth number

School of Computer Science, University of Waterloo. Retrieved 15 February 2024. "Journal of Integer Sequences". Cheriton School of Computer Science. Retrieved

In computer science, a linked list is a linear collection of data elements whose order is not given by their physical placement in memory. Instead, each

formally specifying system behavior. It was a very active subject of computer science research around 1980. Algebraic specification seeks to systematically

from logic to statistical physics and from evolutionary biology to computer science. Combinatorics is well known for the breadth of the problems it tackles

can be determined in polynomial time is a major unsolved problem in computer science, known as the graph isomorphism problem. The two graphs shown below

In mathematics and computer science, optimal addition-chain exponentiation is a method of exponentiation by a positive integer power that requires a minimal

calculated the highest proper divisor of 218 (262,144), by testing every integer from 218 downwards. This algorithm would take a long time to execute—and

the term comes from mathematics use, rather than the prior use in computer science. The authors consider this overlap in terminology to be "unfortunate

In computer science and software programming, a value is the representation of some entity that can be manipulated by a program. The members of a type

software suite developed by Google for solving linear programming (LP), mixed integer programming (MIP), constraint programming (CP), vehicle routing (VRP),

affects various areas of mathematical study, including algebra and computer science. There have been a wide range of contributions to the field. Some of

orthogonal drawings of planar graphs, in which the vertices are placed in an integer lattice and the edges are drawn as axis-aligned polylines, could be performed

In computer science, a simple precedence parser is a type of bottom-up parser for context-free grammars that can be used only by simple precedence grammars

In computer science, the complexity function of a word or string (a finite or infinite sequence of symbols from some alphabet) is the function that counts

In algorithmic information theory (a subfield of computer science and mathematics), the Kolmogorov complexity of an object, such as a piece of text, is

{\sqrt {3}}} ⁠ apart in the integer lattice; the edges of the diamond structure lie along the body diagonals of the integer grid cubes. This structure

tree structures in specific fields, see Tree (data structure) for computer science; insofar as it relates to graph theory, see tree (graph theory) or

A default, in computer science, refers to the preexisting value of a user-configurable setting that is assigned to a software application, computer program

of two or more integers, which are not all zero, is the largest positive integer that divides each of the integers. For two integers x, y, the greatest

15th Symposium on Mathematical Foundations of Computer Science (MFCS 1990). Lecture Notes in Computer Science, Vol. 452, pages 313–321, doi:10.1007/BFb0029624

+ 1 n) for all integers d > 0. If polyL had a complete problem, call it A, it would be an element of DSPACE(logk n) for some integer k > 0. Suppose problem

In number theory, the radical of a positive integer n is defined as the product of the distinct prime numbers dividing n. Each prime factor of n occurs

the growth rate r, as time t goes on in discrete intervals (that is, at integer times 0, 1, 2, 3, ...), is x t = x 0 ( 1 + r ) t {\displaystyle x_{t}=x_{0}(1+r)^{t}}

come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete

orderings are counted by the ordered Bell numbers. They are used in computer science as part of partition refinement algorithms, and in the C++ Standard

A default, in computer science, refers to the preexisting value of a user-configurable setting that is assigned to a software application, computer program

would be the optimal bound, although this remains a conjecture today. Integer multiplication algorithms can also be used to multiply polynomials by means

small integers with low memory requirements. In computer science, Willard is best known for his work with Michael Fredman in the early 1990s on integer sorting

come from many areas of mathematics, such as theoretical physics, computer science, algebra, analysis, combinatorics, algebraic, differential, discrete

a strongly NP-complete problem in computer science. The problem is to decide whether a given multiset of integers can be partitioned into triplets that

theory and computer science, the partition problem, or number partitioning, is the task of deciding whether a given multiset S of positive integers can be

is a decision problem in computer science. In its most general formulation, there is a multiset S {\displaystyle S} of integers and a target-sum T {\displaystyle

at the Massachusetts Institute of Technology (MIT) Laboratory for Computer Science with support from the European Commission, and the Defense Advanced

mathematics, publishing papers in the fields of combinatorics and computer science. It started in 1981, with László Babai and László Lovász as the editors-in-chief

In computer science, a type system is nominal (also called nominative or name-based) if compatibility and equivalence of data types is determined by explicit

satisfiability problem (SAT), and is of importance to theoretical computer science, being the first problem shown to be NP-complete. The closely related

{P} } and the set of integers Z {\displaystyle \mathbb {Z} } , in which each prime p {\displaystyle p} is related to each integer z {\displaystyle z} that

In computer science and information theory, a canonical Huffman code is a particular type of Huffman code with unique properties which allow it to be described

scientist John McCarthy as a test case for formal verification within computer science. The McCarthy 91 function is defined as M ( n ) = { n − 10 , if  n

and Faster Integer Programming". Hildebrand, Robert (2016-10-07). "FPT algorithm for mixed integer program". Theoretical Computer Science Stack Exchange

trial division, tests whether ⁠ n {\displaystyle n} ⁠ is a multiple of any integer between 2 and ⁠ n {\displaystyle {\sqrt {n}}} ⁠. Faster algorithms include

Eugene Edward McDonnell (October 18, 1926 – August 17, 2010) was a computer science pioneer and long-time contributor to the programming language siblings

calculate the determinant or the echelon form of a matrix with integer entries using only integer arithmetic; any divisions that are performed are guaranteed

Encyclopedia of Integer Sequences. OEIS Foundation. Sloane, N. J. A. (ed.). "Sequence A000566 (Heptagonal numbers)". The On-Line Encyclopedia of Integer Sequences

Presburger's Article on Integer Arithmetic: Remarks and Translation (PDF) (Technical Report). Vol. TR84-639. Ithaca/NY: Dept. of Computer Science, Cornell University

In computer science, software pipelining is a technique used to optimize loops, in a manner that parallels hardware pipelining. Software pipelining is

In computer science, abstract interpretation is a theory of sound approximation of the semantics of computer programs, based on monotonic functions over

In computer science, control flow (or flow of control) is the order in which individual statements, instructions or function calls of an imperative program

In computer science, a y-fast trie is a data structure for storing integers from a bounded domain. It supports exact and predecessor or successor queries

space. An elementary example of a random walk is the random walk on the integer number line Z {\displaystyle \mathbb {Z} } which starts at 0, and at each

secure coding principles and risk analysis into the undergraduate computer science and information systems curriculum". Proceedings of the 3rd annual

cryptography exists at the intersection of the disciplines of mathematics, computer science, information security, electrical engineering, digital signal processing

In computer science, parameterized complexity is a branch of computational complexity theory that focuses on classifying computational problems according

In the formal language theory of computer science, left recursion is a special case of recursion where a string is recognized as part of a language by

In computer science, a logical shift is a bitwise operation that shifts all the bits of its operand. The two base variants are the logical left shift and

Source Software Journal of Statistical Software Logical Methods in Computer Science Semantic Web Theory of Computing Transactions on Graph Data and Knowledge

In computer science, in particular in formal language theory, the pumping lemma for context-free languages, also known as the Bar-Hillel lemma, is a lemma

In computer science, the computational complexity or simply complexity of an algorithm is the amount of resources required to run it. Particular focus

A non-integer representation uses non-integer numbers as the radix, or base, of a positional numeral system. For a non-integer radix β > 1, the value of

minimal set of integer vectors in C such that every integer vector in C is a conical combination of the vectors in the Hilbert basis with integer coefficients

a hypothetical integer factorization device described in 1999 by Adi Shamir and purported to be capable of factoring 512-bit integers. It is also a pun

such as physics, engineering, medicine, biology, finance, business, computer science, and industry. Thus, applied mathematics is a combination of mathematical

(x)\sim {\frac {x}{\ln x}}.} Asymptotic analysis is commonly used in computer science as part of the analysis of algorithms and is often expressed there

is the lowest unsigned integer value, one of the most fundamental types in programming and hardware design. In computer science, zero is thus often used

In computer science, binary search, also known as half-interval search, logarithmic search, or binary chop, is a search algorithm that finds the position

Register Allocation Using Integer Linear Programming". Languages and Compilers for Parallel Computing. Lecture Notes in Computer Science. Vol. 4382. pp. 267–282

{b} _{1},\mathbf {b} _{2},\dots ,\mathbf {b} _{d}\}} with n-dimensional integer coordinates, for a lattice L (a discrete subgroup of Rn) with d ≤ n {\displaystyle

Bertrand's Postulate". Journal of Integer Sequences. 1. Waterloo, ON: David R. Cheriton School of Computer Science: Article 98.1.2. MR 1677070. S2CID 230430995

In computer science and data mining, MinHash (or the min-wise independent permutations locality sensitive hashing scheme) is a technique for quickly estimating

In mathematics and theoretical computer science, an automatic sequence (also called a k-automatic sequence or a k-recognizable sequence when one wants

complexity of membership problems for circuits over sets of integers", Theoretical Computer Science, 369 (1) (1–3 ed.), Essex, UK: Elsevier Science Publishers

In computer science, an implicit data structure or space-efficient data structure is a data structure that stores very little information other than the

In computer science, an implicit data structure or space-efficient data structure is a data structure that stores very little information other than the

In mathematics and computer science, the critical exponent of a finite or infinite sequence of symbols over a finite alphabet describes the largest number

Sessions with Failure in Rust". Electronic Proceedings in Theoretical Computer Science. 304: 48–60. arXiv:1909.05970. doi:10.4204/EPTCS.304.4. ISSN 2075-2180

this is most often a number – for example, a real number such as π or an integer such as 42. The value of a variable or a constant is any number or other

for which only integer solutions are sought. In this case, the solution set is the empty set, since 2 is not the square of an integer. However, if one

CiteSeer search engine listed the book as the most cited reference in computer science literature. Another appendix of the book featured problems for which

NP-hard problem in combinatorial optimization, important in theoretical computer science and operations research. The travelling purchaser problem, the vehicle

algorithms. The exact solution to this problem can be formulated using integer programming. Alternatively, if the number of reversed edges is very small

extensively in computer science. In some computer programming languages, the size in bits of certain data types 16-bit computing A 16-bit integer can represent

over any cyclic group G {\displaystyle G} , like multiplicative group of integers modulo n if and only if n is 1, 2, 4, pk or 2pk, where p is an odd prime

In computer science, heapsort is an efficient, comparison-based sorting algorithm that reorganizes an input array into a heap (a data structure where each

In theoretical computer science, a pointer machine is an atomistic abstract computational machine whose storage structure is a graph. A pointer algorithm

In computer science, local search is a heuristic method for solving computationally hard optimization problems. Local search can be used on problems that

quadratic Frobenius test (EQFT). Let n be a positive integer such that n is odd, and let b and c be integers such that ( b 2 + 4 c n ) = − 1 {\displaystyle

(2002), "Integer sorting in O(n√log log n) expected time and linear space", Proceedings of the 43rd Annual Symposium on Foundations of Computer Science (FOCS

{\displaystyle X_{0},\,0\leq X_{0}<m} — the "seed" or "start value" are integer constants that specify the generator. If c = 0, the generator is often

In computer science, a radix tree (also radix trie or compact prefix tree or compressed trie) is a data structure that represents a space-optimized trie

programming Information Leak Prevention Instruction-level parallelism Integer linear programming ilp., a 2013 album by Kwes Independent Labour Party

automaton is an abstract machine used in a formal logic and theoretical computer science to model computation. It is the most primitive of the four types of

base number). This mathematical operation is primarily of interest in computer science, where it has varying effects depending on how a specific computer

resources among multiple threads by means of mutual exclusion. In computer science, it is common for multiple threads to simultaneously access the same

31st Int. Worksh. Graph-Theoretic Concepts in Computer Science (WG 2005), Lecture Notes in Computer Science, vol. 3787, Springer-Verlag, pp. 59–68, CiteSeerX 10

Leopold Kronecker) is a function of two variables, usually just non-negative integers. The function is 1 if the variables are equal, and 0 otherwise: δ i j =

product of two large and unknown primes into the constituent primes. The integer factorization problem is believed to be intractable on any conventional

memory locations. Those address-generation calculations involve different integer arithmetic operations, such as addition, subtraction, modulo operations

Štefan Porubský, "Integer rounding functions", Interactive Information Portal for Algorithmic Mathematics, Institute of Computer Science of the Czech Academy

degree in computer science in 1988 from University Paris VII and a magister from École Normale Supérieure in mathematics and computer science. His doctoral

implementation for (f integer y), where y matches all types. (defmethod f ((x integer) y) 1) (f 1 2.0) => 1 ; Define an implementation for (f integer real). (defmethod

In computer science, a tail call is a subroutine call performed as the final action of a procedure. If the target of a tail is the same subroutine, the

In computer science, a linked data structure is a data structure which consists of a set of data records (nodes) linked together and organized by references

Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development

Ontario, Canada. It was designed to help students taking their first computer science course learn how to code. Turing is a descendant of Pascal, Euclid

Integer arithmetic is about calculations with positive and negative integers. Rational number arithmetic involves operations on fractions of integers

classical algorithm known for factoring integers larger than 10100. Heuristically, its complexity for factoring an integer n (consisting of ⌊log2 n⌋ + 1 bits)

hence nonelementary). A vector addition system consists of a finite set of integer vectors with all vectors having the same length. An initial vector is seen

Techniques". Other Finalists: Georgina Hall and Yair Carmon List of computer science awards Date, Issue (August 8, 2005). Efficient graph algorithms for

In computer science, a monotone priority queue is a variant of the priority queue abstract data type in which the priorities of extracted items are required

factorial of a number n, denoted by n‼, is the product of all the positive integers up to n that have the same parity (odd or even) as n. That is, n ! ! =

corresponding integer sublattice L ( I ) ⊆ Z n {\displaystyle {\mathcal {L}}(I)\subseteq \mathbb {Z} ^{n}} . An ideal lattice is an integer lattice L (

Jong-Shi; Stone, Richard E. (1992). The linear complementarity problem. Computer Science and Scientific Computing. Boston, MA: Academic Press, Inc. pp. xxiv+762

numbers, multiply by 3 and add 1. With enough repetition, do all positive integers converge to 1? (more unsolved problems in mathematics) The Collatz conjecture

development on and with Racket. Racket is also used for scripting, computer science education, and research. The Racket platform provides an implementation

progressions are of interest in number theory, combinatorics, and computer science, both from theoretical and applied points of view. Find the cardinality

on the interpretation of the exponent, the significand may represent an integer or a fractional number, which may cause the term "mantissa" to be misleading

element is aperiodic, that is, for each x in S there exists a positive integer n such that xn = xn+1. An aperiodic monoid is an aperiodic semigroup which

{\displaystyle \mathbb {R} ^{n}} , the subgroup of all linear combinations with integer coefficients of the basis vectors forms a lattice, and every lattice can

every non-empty subset of nonnegative integers contains a least element. In other words, the set of nonnegative integers is well-ordered by its "natural" or

progressions are of interest in number theory, combinatorics, and computer science, both from theoretical and applied points of view. Find the cardinality

element is aperiodic, that is, for each x in S there exists a positive integer n such that xn = xn+1. An aperiodic monoid is an aperiodic semigroup which

circles. The problem of counting integer points in convex polyhedra arises in several areas of mathematics and computer science. In application areas, the dot

the code. /* store integer variable "i" in RAM, register, or other location as compiler sees fit */ int i; /* suggests storing integer variable "i" in a

In computer science, a circular buffer, circular queue, cyclic buffer or ring buffer is a data structure that uses a single, fixed-size buffer as if it

{1}{5+2\times 5+5+2\times 5+10+0+3+4}}=0.98} Cohesion (computer science) Connascence (computer science) Coupling (physics) Dead code elimination Dependency

maximum degree is minimal. The decision problem is: Given a graph G and an integer k, does G have a spanning tree such that no vertex has degree greater than

checking the correctness of various program constraints. For example, that an integer variable is greater-than-zero, or lies between the bounds of an array.

2001 was dedicated to him. Jack's son Jeff Edmonds is a professor of computer science at York University, and his wife Kathie Cameron is a professor of mathematics

others followed up on this work. Design patterns gained popularity in computer science after the book Design Patterns: Elements of Reusable Object-Oriented

Unsolved problem in computer science: Is there an algorithm to solve the 3SUM problem in time O ( n 2 − ϵ ) {\displaystyle O(n^{2-\epsilon })} , for some

equal sizes. There are q − 1 partitions of the q-quantiles, one for each integer k satisfying 0 < k < q. In some cases the value of a quantile may not be

requires software to represent the objects of this framework (sets of integer-valued points in regions of various spaces) and perform operations upon

divides y" between integers, polynomials, or elements of a commutative ring. For example, the divides relation is reflexive as every integer divides itself

In computer science, imperative programming is a programming paradigm of software that uses statements that change a program's state. In much the same

← empty_list for k = 1 , 2 , … {\displaystyle k=1,2,\ldots } Using an integer factorization algorithm optimized for smooth numbers, try to factor g k

code[citation needed] which encodes positive integers into binary code words. It is one example of representations of integers based on Fibonacci numbers. Each code

Koblitz Curves Using Kleinian Integers", Cryptographic Hardware and Embedded Systems - CHES 2006, Lecture Notes in Computer Science, vol. 4249, pp. 445–459

twā would thus be /twɑː/, /twɔː/, /twoː/, /twuː/, and finally /tuː/. An integer is determined to be even if it is divisible by two. When written in base

date of grade, grade>. The user and movie fields are integer IDs, while grades are from 1 to 5 (integer) stars. The qualifying data set contains over 2,817

combinatorial cube. They have applications in Ramsey theory and in computer science in the detection of duplicate code. Formally, a k {\displaystyle k}

In computer science, cycle detection or cycle finding is the algorithmic problem of finding a cycle in a sequence of iterated function values. For any

invert the OU function is proven to be as hard as factoring a composite integer public key. There are three versions of EPOC: EPOC-1 uses a one-way trapdoor

In computer science, a for-loop or for loop is a control flow statement for specifying iteration. Specifically, a for-loop functions by running a section

a dependently-typed 3-tuple is two integers and a proof that the first integer is smaller than the second integer, described by the type: ∑ m : Z ∑ n

unchanged; in mathematical terminology, 0 is the additive identity of the integers, rational numbers, real numbers, and complex numbers, as well as other

first parameter and a covariant functor in the second. Polymorphism (computer science) Inheritance (object-oriented programming) Liskov substitution principle

value down to zero. The V() operation increases the semaphore value. begin integer number of queueing portions, number of empty positions, buffer manipulation;

topology, is a subfield of topology with an overlap with areas of computer science, in particular, computational geometry and computational complexity

In computer science, a binary decision diagram (BDD) or branching program is a data structure that is used to represent a Boolean function. On a more abstract

Jack; Holzman, Albert G; Kent, Allen, eds. (1979). Encyclopedia of Computer Science and Technology: Volume 12. Marcel Dekker, inc. p. 164. ISBN 0-8247-2262-0

fractions – a generalization of rational functions that allows taking integer roots Rudin, Walter (1987). Real and Complex Analysis. New York, NY: McGraw-Hill

implementation and a security guarantee relative to the difficulty of integer factorization, which has not been proven for RSA. However, Rabin signatures

In computer science, a deterministic acyclic finite state automaton (DAFSA), is a data structure that represents a set of strings, and allows for a query

that includes at least one endpoint of every edge of the graph. In computer science, the problem of finding a minimum vertex cover is a classical optimization

In mathematics and computer science, an algorithm (/ˈælɡərɪðəm/ ) is a finite sequence of mathematically rigorous instructions, typically used to solve

In computer science and operations research, randomized rounding is a widely used approach for designing and analyzing approximation algorithms. Many combinatorial

scheduling represents a complex optimization challenge within the fields of computer science and operations research, specifically categorized under combinatorial

contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. The term fuzzy logic was introduced with the 1965 proposal

algebra, and play a prominent role in engineering, physics, chemistry, computer science, and economics. A system of non-linear equations can often be approximated

algebra, and play a prominent role in engineering, physics, chemistry, computer science, and economics. A system of non-linear equations can often be approximated

In logic and computer science, the Boolean satisfiability problem (sometimes called propositional satisfiability problem and abbreviated SATISFIABILITY

object is constant on families or invariant under change of metric). In computer science, an invariant is a logical assertion that is always held to be true

Swierczewski, an IT student at the College of Computer Science and Business Administration in Łomża, Computer Science and Automation Institute. As of 2016 it

factorization method (ECM) is a fast, sub-exponential running time, algorithm for integer factorization, which employs elliptic curves. For general-purpose factoring

never used in practice, galactic algorithms may still contribute to computer science: An algorithm, even if impractical, may show new techniques that may

be a polynomial with integer (or p-adic integer) coefficients, and let m,k be positive integers such that m ≤ k. If r is an integer such that f ( r ) ≡

contrast, in Boolean logic, the truth values of variables may only be the integer values 0 or 1. The term fuzzy logic was introduced with the 1965 proposal

derivative. The binary logarithm uses base 2 and is widely used in computer science, information theory, music theory, and photography. When the base is

to x, y and z, respectively, make the sentence true. The non-negative integer n that gives the number of "places" in the relation is called the arity

Unknowability Leeuwen, Jan van, ed. (1998). Handbook of Theoretical Computer Science. Vol. A, Algorithms and complexity. Amsterdam: Elsevier. ISBN 0262720140

problems find innumerable applications in artificial intelligence and computer science. They are also variously referred to as markov random fields (in statistics

In mathematical logic and theoretical computer science, a register machine is a generic class of abstract machines, analogous to a Turing machine and thus

defined on an arbitrary totally ordered set, such as integers or rational numbers. The notation of integer intervals is considered in the special section below

this, Poly1305: Interprets r {\displaystyle r} as a little-endian 16-byte integer. Breaks the message m = ( m [ 0 ] , m [ 1 ] , m [ 2 ] , … , m [ L − 1 ]

functor is a synonym for function symbol. Callback (computer science) Closure (computer science) Function pointer Higher-order function Command pattern

sieves are most common. A prime sieve works by creating a list of all integers up to a desired limit and progressively removing composite numbers (which

a 32-bit signed integer may be used to hold a 16-bit unsigned value losslessly, and a 64-bit signed integer a 32-bit unsigned integer, there is no larger

DatalogZ (stylized as Datalogℤ) is an extension of Datalog with integer arithmetic and comparisons. The decision problem of whether or not a given ground

In computer science, the matrix mortality problem (or mortal matrix problem) is a decision problem that asks, given a finite set of n×n matrices with integer

In logic and computer science, specifically automated reasoning, unification is an algorithmic process of solving equations between symbolic expressions

Petri Nets I: Basic Models – Advances in Petri Nets. Lecture Notes in Computer Science. Vol. 1491. Springer. pp. 12–121. doi:10.1007/3-540-65306-6_14. ISBN 3-540-65306-6

(for hashing integers, vectors, strings), and their evaluation is often very efficient. Universal hashing has numerous uses in computer science, for example

constants used in the functions below //uint64_t is an unsigned 64-bit integer variable type (defined in C99 version of C language) const uint64_t m1

the Germanic concept of 1200 as a long thousand. It is the first 4-digit integer. The decimal representation for one thousand is 1000—a one followed by

spent a few years of employment in the industry before he switched to computer science: from 1987 to 2000 at Utrecht University and since 2000 at Eindhoven

This is a list of computer scientists, people who do work in computer science, in particular researchers and authors. Some persons notable as programmers

from such vendors differ on implementing data-format support, such as integer and floating-point formats (32-bit and 64-bit). Microsoft introduced a

polynomials over the integers. Given positive integers A , B , C {\displaystyle \textstyle A,B,C} , decide existence of positive integers x , y {\displaystyle

Language Engineering and Rigorous Software Development. Lecture Notes in Computer Science. Vol. 5520. pp. 57–99. doi:10.1007/978-3-642-03153-3_2. ISBN 978-3-642-03152-6

This is the case whether or not it is interpreted as a floating-point or integer value. The purpose of this is to enable high speed comparisons between

subtypes of List<String>: PayloadList<String, String> PayloadList<String, Integer> PayloadList<String, Exception> Liskov substitution principle explains

Dixon's random squares method or Dixon's algorithm) is a general-purpose integer factorization algorithm; it is the prototypical factor base method. Unlike

In computer science, brute-force search or exhaustive search, also known as generate and test, is a very general problem-solving technique and algorithmic

In computer science and mathematics, the Josephus problem (or Josephus permutation) is a theoretical problem related to a certain counting-out game. Such

Foundations of Software Technology and Theoretical Computer Science, Lecture Notes in Computer Science, vol. 652, Springer-Verlag, pp. 128–139. Reischuk

dimensions, it is possible to define a height function associating an integer to the vertices of the grid. For instance, draw a chessboard, fix a node

model checking Type inhabitation problem for simply typed lambda calculus Integer circuit evaluation Word problem for linear bounded automata Word problem

In computer science, an instruction set architecture (ISA) is an abstract model that generally defines how software controls the CPU in a computer or a

factoring". Advances in Cryptology – EUROCRYPT'98. Lecture Notes in Computer Science. Vol. 1403. Springer. pp. 59–71. doi:10.1007/BFb0054117. ISBN 978-3-540-64518-4

Ackermann's publication of his function (which had three non-negative integer arguments), many authors modified it to suit various purposes, so that

In computer science, multiway number partitioning is the problem of partitioning a multiset of numbers into a fixed number of subsets, such that the sums

Mixed Integer Nonlinear Programming (Springer, 2012), Integer Programming and Combinatorial Optimization (Lecture Notes in Computer Science, Vol. 8494;

In computer science and mathematics, confluence is a property of rewriting systems, describing which terms in such a system can be rewritten in more than

Short integer solution (SIS) and ring-SIS problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based

instances of the laws can be opened by clicking on [show]; they use lists of integer numbers, addition, minus, and multiplication. The notation in Bird's paper

In mathematics, the Dedekind numbers are a rapidly growing sequence of integers named after Richard Dedekind, who defined them in 1897. The Dedekind number

as number theory, linear algebra, and real analysis, as well as in computer science (e.g. randomized rounding), and information theory. If every object

Short integer solution (SIS) and ring-SIS problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based

examples. ECS combines orthogonal, well-established ideas in general computer science and programming language theory. For example, components can be seen

method of combinatorial optimization for solving integer linear programming (ILP) and mixed integer linear programming (MILP) problems with many variables

base g = 5 (which is a primitive root modulo 23). Alice chooses a secret integer a = 4, then sends Bob A = ga mod p A = 54 mod 23 = 4 (in this example both

asks which sets of integers have the property that each integer in the set is a proper divisor of the product of the other integers in the set, plus 1

is not algebraic: that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients. The best-known transcendental

{\displaystyle n^{2}} and ( n + 1 ) 2 {\displaystyle (n+1)^{2}} for every positive integer n {\displaystyle n} . The conjecture is one of Landau's problems (1912)

The language itself was an extended version of ALGOL 60. It supported integers, single- and double-precision floating point and complex numbers, and both

In information theory and computer science, the Damerau–Levenshtein distance (named after Frederick J. Damerau and Vladimir I. Levenshtein) is a string

In computer science, the Knuth–Morris–Pratt algorithm (or KMP algorithm) is a string-searching algorithm that searches for occurrences of a "word" W within

(computer science): agreeing on a single value or history among unreliable processors Chandra–Toueg consensus algorithm Paxos algorithm Raft (computer

In computer science, attack patterns are a group of rigorous methods for finding bugs or errors in code related to computer security. Attack patterns are

computation, although faster randomized algorithms exist for points with integer coordinates. For points in higher dimensions, finding an optimal algorithm

Satterthwaite, Edwin H. (March 1968). Technical Report Number: CS-TR-68-89. Computer Science Department (Report). Stanford University. (Various documents for Stanford's

In logic, philosophy, and theoretical computer science, dynamic logic is an extension of modal logic capable of encoding properties of computer programs

demonstrations that many natural computational problems occurring throughout computer science are computationally intractable, and it drove interest in the study

complexity of algorithms for difficult number theory problems, e.g. sieves for integer factorization and methods for solving discrete logarithms. The benefit

In mathematical logic and computer science the symbol ⊢ ( ⊢ {\displaystyle \vdash } ) has taken the name turnstile because of its resemblance to a typical

and boundedness problems for vector addition systems". Theoretical Computer Science: 223–231. Lipton, R. (1976). "The Reachability Problem Requires Exponential

In theoretical computer science and formal language theory, a regular language (also called a rational language) is a formal language that can be defined

it is practical to find three very large positive integers e, d, and n, such that for all integers m (0 ≤ m < n), both ( m e ) d {\displaystyle (m^{e})^{d}}

Append integer value '5' to vector 'items'. items.push_back(2); // Append integer value '2' to vector 'items'. items.push_back(9); // Append integer value

supported system locales and be greater or equal in size to char, wint_t Integer type that can hold any value of a wchar_t as well as the value of the macro

Emeritus at Stanford University, who was an early pioneer in the field of computer science. Since 1969, Pratt has made several contributions to foundational areas

chess board in computer chess programs. The number 0x88 is a hexadecimal integer (13610, 2108, 100010002). The rank and file positions are each represented

= numerator = 0 while (integer_part < array.size) // get the ranges for A and B start = integer_part integer_part += integer_step numerator += numerator_step

having an associated arity (i.e. number of inputs). For any non-negative integer n {\displaystyle n} , let τ n {\displaystyle \tau _{n}} denote the function

essential in the natural sciences, engineering, medicine, finance, computer science, and the social sciences. Although mathematics is extensively used

In computer science, a three-way comparison takes two values A and B belonging to a type with a total order and determines whether A < B, A = B, or A >

instance, every polyhedral graph is the graph of a convex polyhedron with integer coordinates, or the graph of a convex polyhedron all of whose edges are

simplification used in mathematical logic, model theory, and theoretical computer science. Informally, a quantified statement " ∃ x {\displaystyle \exists x}

:\mathbb {N} \to \mathbb {R} } such that for every positive integer c there exists an integer Nc such that for all x > Nc, | μ ( x ) | < 1 x c . {\displaystyle

In computer science, the Rabin–Karp algorithm or Karp–Rabin algorithm is a string-searching algorithm created by Richard M. Karp and Michael O. Rabin (1987)

conference proceedings papers is a particular problem for scholars in computer science, where conference proceedings are considered an important part of the

In computer science, the iterated logarithm of n {\displaystyle n} , written log*  n {\displaystyle n} (usually read "log star"), is the number of times

relation: b n ≡ b ( mod n ) {\displaystyle b^{n}\equiv b{\pmod {n}}} for all integers ⁠ b {\displaystyle b} ⁠. The relation may also be expressed in the form:

a performance cost. Programming language theory is the subfield of computer science that studies the design, implementation, analysis, characterization

"Robert W Floyd, In Memoriam", by Donald E. Knuth, 2003 - (on the influence of Bob Floyd) TAoCP and its Influence of Computer Science (Softpanorama)

Jong-Shi; Stone, Richard E. (1992). The linear complementarity problem. Computer Science and Scientific Computing. Boston, MA: Academic Press, Inc. pp. xxiv+762

lattices have many applications inside of lattice theory, theoretical computer science, cryptography and mathematics more broadly. For instance, it is used

In theoretical computer science, the time complexity is the computational complexity that describes the amount of computer time it takes to run an algorithm

September 2, 1994) was an American computer scientist and a professor of computer science at the University of California, Berkeley. Lawler came to Harvard as

Bachmann to stand for Ordnung, meaning the order of approximation. In computer science, big O notation is used to classify algorithms according to how their

Creating a program to find a knight's tour is a common problem given to computer science students. Variations of the knight's tour problem involve chessboards

number theory, Euler's totient function counts the positive integers up to a given integer n that are relatively prime to n. It is written using the Greek

Scientist and a professor of Computer Science at Pennsylvania State University. He is mostly known for his work on fast integer multiplication. One of Fürer's

of computer science at the University of California, Berkeley until 2001. From 2001 to 2018, he was the Bruce Nelson Professor of Computer Science at

design ideas for the language came from Craig's Master's thesis in computer science at the University of Toronto. Craig's thesis was heavily influenced

roots modulo composite numbers is a computational problem equivalent to integer factorization. An equivalent, but slightly more redundant version of this

In theoretical computer science, circuit complexity is a branch of computational complexity theory in which Boolean functions are classified according

efficiently solvable by deterministic classical computers. For instance, integer factorization and the discrete logarithm problem are known to be in BQP

them, is a positive integer of the form: F n = 2 2 n + 1 , {\displaystyle F_{n}=2^{2^{n}}+1,} where n is a non-negative integer. The first few Fermat

one of the interfaces of the Linux kernel. The x32 ABI provides 32-bit integers, long and pointers (ILP32) on Intel and AMD 64-bit hardware. The ABI allows

the number of boxes in each row gives a partition λ of a non-negative integer n, the total number of boxes of the diagram. The Young diagram is said

numbers. The website was created in 1998 by Mads Haahr, a doctor and computer science professor at Trinity College in Dublin, Ireland. Random numbers are

Scientist and a professor of Computer Science at Pennsylvania State University. He is mostly known for his work on fast integer multiplication. One of Fürer's

In computer science, data stream clustering is defined as the clustering of data that arrive continuously such as telephone records, multimedia data, financial

The multiple subset sum problem is an optimization problem in computer science and operations research. It is a generalization of the subset sum problem

recent standards have used integer-based transforms that have similar properties to the DCT but are explicitly based on integer processing rather than being

In computer science, a math library (or maths library) is a component of a programming language's standard library containing functions (or subroutines)

of Computer Science 2015 – MFCS 2015: 40th International Symposium, Milan, Italy, August 24-28, 2015, Proceedings, Lecture Notes in Computer Science, vol

Crane, Linda. "In Memoriam: David S. Johnson". Columbia University Computer Science. Columbia University. Retrieved 9 March 2016. "David S. Johnson Named

this relationship is impossible to satisfy when p and q are restricted to integer numbers isn't obvious, but it has been known since ancient times and has

System from Unodecimal to Vigesimal" (PDF). International Journal of Computer Science and Telecommunications. 3 (1). London: Sysbase Solution Ltd.: 13. Rawat

In computer science, a tagged architecture is a type of computer architecture where every word of memory constitutes a tagged union, being divided into

Ta(n) or Taxicab(n), is defined as the smallest integer that can be expressed as a sum of two positive integer cubes in n distinct ways. The most famous taxicab

In computer science, a loop invariant is a property of a program loop that is true before (and after) each iteration. It is a logical assertion, sometimes

University of Mining and Technology (2013) Chaired Research Professor in Computer Science (Chaire d’excellence, Pays de la Loire), Laboratoire d'Etude et de

practical applications in diverse fields of applied mathematics and computer science, such as configuration spaces, homology computation, denoising, mesh

In computer science, register transfer language (RTL) is a kind of intermediate representation (IR) that is very close to assembly language, such as that

parallel programs, which implemented methods for common problems in computer science. This experimentation allowed him to make the following conclusions

In computer science, the analysis of algorithms is the process of finding the computational complexity of algorithms—the amount of time, storage, or other

roots of −1. The real numbers include the rational numbers, such as the integer −5 and the fraction 4 / 3. The rest of the real numbers are called irrational

Originally run at 133 MHz, but later certified at 200 MHz Each core has an integer divider peripheral and two interpolators 264 KB SRAM in six independent

and computer science, the term can be used in several ways: In computing, it is typically the modulo operation: given two numbers (either integer or real)

In computer science, functional programming is a programming paradigm where programs are constructed by applying and composing functions. It is a declarative

pseudorandom number generation. She was a distinguished career professor of computer science at Carnegie Mellon University until 2019 and is currently a professor

consisting of a private key d {\displaystyle d} (a randomly selected integer in the interval [ 1 , n − 1 ] {\displaystyle [1,n-1]} ) and a public key

sphere, given by the points (x,y,w) with x2+y2+w2=1. Let n be a nonnegative integer. The (analytical model of, or canonical) oriented (real) projective space

version runs in linear time: Lazy<Integer> a = () -> 1; for (int i = 0; i < 10; i++) { Lazy<Integer> b = a; a = new Memo<Integer>(() -> b.eval() + b.eval());

arithmetic progressions in subsets of the integers. In 1936, Erdős and Turán conjectured that every set of integers A with positive natural density contains

In computer science, the Edmonds–Karp algorithm is an implementation of the Ford–Fulkerson method for computing the maximum flow in a flow network in O

In computer science, bogosort (also known as permutation sort and stupid sort) is a sorting algorithm based on the generate and test paradigm. The function

Graham; Knuth; Patashnik (1994). Concrete Mathematics: A Foundation for Computer Science (2nd ed.). Addison-Wesley. pp. 267–272. Hsu, Leetsch C.; Jau-Shyong

real-valued or mixed-integer decision variables, EAs such as the evolution strategy or the real-coded GAs are suited. In the case of mixed-integer values, rounding

adjective which corresponds to squaring is quadratic. The square of an integer may also be called a square number or a perfect square. In algebra, the

In computer science, a polynomial-time algorithm is – generally speaking – an algorithm whose running time is upper-bounded by some polynomial function

Report / Faculty of Mathematics and Computer Science. Vol. IR-267. Amsterdam: Faculty of Mathematics and Computer Science, Vrije Universiteit. CiteSeerX 10

In computer science and operations research, approximation algorithms are efficient algorithms that find approximate solutions to optimization problems

the positive integers that occur as coefficients in the binomial theorem. Commonly, a binomial coefficient is indexed by a pair of integers n ≥ k ≥ 0 and

keys are elements of G 2 {\displaystyle G_{2}} , and the secret key is an integer in [ 0 , q − 1 ] {\displaystyle [0,q-1]} . Working in an elliptic curve

In computer science, streaming algorithms are algorithms for processing data streams in which the input is presented as a sequence of items and can be

In computer science and software engineering, busy-waiting, busy-looping or spinning is a technique in which a process repeatedly checks to see if a condition

In computer science and discrete mathematics, an inversion in a sequence is a pair of elements that are out of their natural order. Let π {\displaystyle