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searching for Reduction (computability theory) 87 found (91 total)

alternate case: reduction (computability theory)

Computability theory (6,425 words) [view diff] no match in snippet view article find links to article

Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated

Decision problem (1,246 words) [view diff] no match in snippet view article find links to article

In computability theory and computational complexity theory, a decision problem is a computational problem that can be posed as a yes–no question on a

Reduction (complexity) (1,658 words) [view diff] no match in snippet view article

In computability theory and computational complexity theory, a reduction is an algorithm for transforming one problem into another problem. A sufficiently

Oracle machine (2,028 words) [view diff] no match in snippet view article find links to article

In complexity theory and computability theory, an oracle machine is an abstract machine used to study decision problems. It can be visualized as a black

Normal form (abstract rewriting) (1,284 words) [view diff] no match in snippet view article

rewriting system has the unique normal form property with respect to reduction (UN→) if for every term reducing to normal forms a and b, a is equal to

List of computability and complexity topics (466 words) [view diff] no match in snippet view article find links to article

list of computability and complexity topics, by Wikipedia page. Computability theory is the part of the theory of computation that deals with what can

Circuit satisfiability problem (1,183 words) [view diff] no match in snippet view article find links to article

been proven to be CoNP-Complete via a reduction from Circuit UNSAT problem. The gadgets constructed for this reduction are: wire, split, AND and NOT gates

Theory of computation (2,168 words) [view diff] no match in snippet view article find links to article

into three major branches: automata theory and formal languages, computability theory, and computational complexity theory, which are linked by the question:

Decider (Turing machine) (1,302 words) [view diff] no match in snippet view article

In computability theory, a decider is a Turing machine that halts for every input. A decider is also called a total Turing machine as it represents a total

Myhill isomorphism theorem (1,122 words) [view diff] no match in snippet view article find links to article

In computability theory the Myhill isomorphism theorem, named after John Myhill, provides a characterization for two numberings to induce the same notion

Turing reduction (1,844 words) [view diff] no match in snippet view article find links to article

In computability theory, a Turing reduction from a decision problem A {\displaystyle A} to a decision problem B {\displaystyle B} is an oracle machine

Computational complexity theory (6,704 words) [view diff] no match in snippet view article find links to article

fields in theoretical computer science are analysis of algorithms and computability theory. A key distinction between analysis of algorithms and computational

Computable isomorphism (180 words) [view diff] no match in snippet view article find links to article

In computability theory two sets A , B {\displaystyle A,B} of natural numbers are computably isomorphic or recursively isomorphic if there exists a total

Ackermann function (7,095 words) [view diff] no match in snippet view article find links to article

In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable

Krivine machine (1,911 words) [view diff] no match in snippet view article find links to article

normal form reduction of a lambda term using call-by-name reduction. Thanks to its formalism, it tells in details how a kind of reduction works and sets

Simple set (539 words) [view diff] no match in snippet view article find links to article

In computability theory, a subset of the natural numbers is called simple if it is computably enumerable (c.e.) and co-infinite (i.e. its complement is

Index set (computability) (703 words) [view diff] no match in snippet view article

In computability theory, index sets describe classes of computable functions; specifically, they give all indices of functions in a certain class, according

Truth-table reduction (676 words) [view diff] no match in snippet view article find links to article

In computability theory a truth-table reduction is a type of reduction from a decision problem A {\displaystyle A} to a decision problem B {\displaystyle

Lambda-mu calculus (842 words) [view diff] no match in snippet view article find links to article

(which is completely different both from the μ operator found in computability theory and from the μ operator of modal μ-calculus) and the bracket operator

Computation in the limit (1,678 words) [view diff] no match in snippet view article find links to article

In computability theory, a function is called limit computable if it is the limit of a uniformly computable sequence of functions. The terms computable

Rice's theorem (1,712 words) [view diff] no match in snippet view article find links to article

In computability theory, Rice's theorem states that all non-trivial semantic properties of programs are undecidable. A semantic property is one about the

Computability (3,293 words) [view diff] no match in snippet view article find links to article

problem by an effective procedure. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer

Medvedev reducibility (152 words) [view diff] no match in snippet view article find links to article

In computability theory, a set P of functions N → N {\displaystyle \mathbb {N} \rightarrow \mathbb {N} } is said to be Medvedev-reducible to another set

Martin measure (386 words) [view diff] no match in snippet view article find links to article

degrees that are "at least as complex" as X {\displaystyle X} under Turing reduction. In order-theoretic terms, the cone of [ X ] {\displaystyle [X]} is the

K-trivial set (1,837 words) [view diff] no match in snippet view article find links to article

studied in the field of algorithmic randomness, which is a subfield of Computability theory and related to algorithmic information theory in computer science

Approximation-preserving reduction (1,497 words) [view diff] no match in snippet view article find links to article

In computability theory and computational complexity theory, especially the study of approximation algorithms, an approximation-preserving reduction is

List of undecidable problems (1,586 words) [view diff] no match in snippet view article find links to article

In computability theory, an undecidable problem is a decision problem for which an effective method (algorithm) to derive the correct answer does not exist

Many-one reduction (1,768 words) [view diff] no match in snippet view article find links to article

In computability theory and computational complexity theory, a many-one reduction (also called mapping reduction) is a reduction that converts instances

Lambda calculus (11,994 words) [view diff] no match in snippet view article find links to article

Lambda calculus consists of constructing lambda terms and performing reduction operations on them. A term is defined as any valid lambda calculus expression

Alpha recursion theory (1,455 words) [view diff] no match in snippet view article find links to article

similar to those of the primitive recursive functions. We say R is a reduction procedure if it is α {\displaystyle \alpha } recursively enumerable and

Halting problem (7,356 words) [view diff] no match in snippet view article find links to article

In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the

Emil Leon Post (1,397 words) [view diff] no match in snippet view article find links to article

known for his work in the field that eventually became known as computability theory. Post was born in Augustów, Suwałki Governorate, Congress Poland

Post correspondence problem (2,521 words) [view diff] no match in snippet view article find links to article

some new problem by reducing from PCP, it often happens that the first reduction one finds is not from PCP itself but from an apparently weaker version

Outline of logic (2,119 words) [view diff] no match in snippet view article find links to article

Non-standard model Normal model Model Semantic consequence Truth value Computability theory – branch of mathematical logic that originated in the 1930s with

Primitive recursive function (7,211 words) [view diff] no match in snippet view article find links to article

In computability theory, a primitive recursive function is, roughly speaking, a function that can be computed by a computer program whose loops are all

Selman's theorem (1,201 words) [view diff] no match in snippet view article find links to article

In computability theory, Selman's theorem is a theorem relating enumeration reducibility with enumerability relative to oracles. It is named after Alan

Computability logic (2,560 words) [view diff] no match in snippet view article find links to article

⊓x(p(x)⊔¬p(x))→⊓x(q(x)⊔¬q(x)) does the same but for the stronger version of Turing reduction where the oracle for p can be queried only once. ⊓x⊔y(q(x)↔p(y)) does

Diophantine set (1,475 words) [view diff] no match in snippet view article find links to article

existential quantification merely reflects the usual applications in computability theory and model theory. It does not matter whether natural numbers refer

Julia Robinson (2,184 words) [view diff] no match in snippet view article find links to article

American mathematician noted for her contributions to the fields of computability theory and computational complexity theory—most notably in decision problems

Uniqueness quantification (848 words) [view diff] no match in snippet view article find links to article

principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable

Kolmogorov complexity (7,565 words) [view diff] no match in snippet view article find links to article

13English 14words". It is also possible to show the non-computability of K by reduction from the non-computability of the halting problem H, since K and H are

S2S (mathematics) (4,618 words) [view diff] no match in snippet view article

large grid minors, which can be used to simulate a Turing machine. By reduction to S2S, the MSO theory of countable orders is decidable, as is the MSO

Decidability (logic) (1,887 words) [view diff] no match in snippet view article

undecidable. This is closely related to the concept of a many-one reduction in computability theory. A property of a theory or logical system weaker than decidability

Confluence (abstract rewriting) (1,744 words) [view diff] no match in snippet view article

39:472-482, 1936 Baader & Nipkow 1998, p. 9. Cooper, S. B. (2004). Computability theory. Boca Raton: Chapman & Hall/CRC. p. 184. ISBN 1584882379. Baader

Amalgamation property (817 words) [view diff] no match in snippet view article find links to article

relation,[clarification needed] and in lambda calculus as a manner of reduction having the Church–Rosser property. An amalgam can be formally defined

Wadge hierarchy (1,336 words) [view diff] no match in snippet view article find links to article

cone lemma from computability theory. The Wadge game is a simple infinite game used to investigate the notion of continuous reduction for subsets of Baire

Algorithm characterizations (8,991 words) [view diff] no match in snippet view article find links to article

statements into a form fit for the engine to work with – in this case the reduction of each proposition to its elementary denials", (3) "Thirdly, there is

Satisfiability (1,500 words) [view diff] no match in snippet view article find links to article

principle Truth predicate Truth value Type Ultraproduct Validity Computability theory Church encoding Church–Turing thesis Computably enumerable Computable

EXPTIME (1,220 words) [view diff] no match in snippet view article find links to article

be solved in polynomial time, by the time hierarchy theorem. In computability theory, one of the basic undecidable problems is the halting problem: deciding

Norman Shapiro (806 words) [view diff] no match in snippet view article find links to article

coined the phrase "strong reducibility" for a computability theory currently called the many-one reduction. His thesis was titled Degrees of Computability

Interaction nets (1,895 words) [view diff] no match in snippet view article find links to article

Models of Computation". Models of Computation: An Introduction to Computability Theory. Springer Science & Business Media. pp. 107–130. ISBN 9781848824348

Combinatory logic (5,301 words) [view diff] no match in snippet view article find links to article

combinatory logic is used as a simplified model of computation, used in computability theory and proof theory. Despite its simplicity, combinatory logic captures

Theory (4,341 words) [view diff] no match in snippet view article find links to article

theory — Choquet theory — Coding theory — Combinatorial game theory — Computability theory — Computational complexity theory — Deformation theory — Dimension

Yuri Matiyasevich (1,057 words) [view diff] no match in snippet view article find links to article

ISSN 0090-4104. S2CID 121919479. Yuri Matiyasevich, Julia Robinson (1975). "Reduction of an arbitrary Diophantine equation to one in 13 unknowns". Acta Arithmetica

Proof theory (2,666 words) [view diff] no match in snippet view article find links to article

the process of normalisation in the natural deduction calculus and beta reduction in the typed lambda calculus. This provides the foundation for the intuitionistic

History of logic (13,249 words) [view diff] no match in snippet view article find links to article

inter-related but separate areas of research: model theory, proof theory, computability theory, and set theory, and its ideas and methods began to influence philosophy

Axiomatic system (1,763 words) [view diff] no match in snippet view article find links to article

theory could be reduced to some collection of axioms. More generally, the reduction of a body of propositions to a particular collection of axioms underlies

Gentzen's consistency proof (1,993 words) [view diff] no match in snippet view article find links to article

false, then there is a least such ordinal. Gentzen defines a notion of "reduction procedure" for proofs in Peano arithmetic. For a given proof, such a procedure

Compactness theorem (1,947 words) [view diff] no match in snippet view article find links to article

{\displaystyle \Sigma .} Barwise compactness theorem Herbrand's theorem – reduction of first-order mathematical logic to propositional logicPages displaying

Substitution (logic) (2,938 words) [view diff] no match in snippet view article

but not identical to, function composition; it is closely related to β-reduction in lambda calculus. In contrast to these notions, however, the accent

Logic (16,460 words) [view diff] no match in snippet view article find links to article

Major subareas include model theory, proof theory, set theory, and computability theory. Research in mathematical logic commonly addresses the mathematical

Function (mathematics) (11,411 words) [view diff] no match in snippet view article

the major open problems in mathematics, the Riemann hypothesis. In computability theory, a general recursive function is a partial function from the integers

Type theory (8,234 words) [view diff] no match in snippet view article find links to article

inference rules known as β {\displaystyle \beta } -reduction and η {\displaystyle \eta } -reduction. They generalize the notion of function application

Model checking (2,788 words) [view diff] no match in snippet view article find links to article

to hardware designs. For software, because of undecidability (see computability theory) the approach cannot be fully algorithmic, apply to all systems,

Propositional formula (11,131 words) [view diff] no match in snippet view article find links to article

they have designed using synthesis techniques and then apply various reduction and minimization techniques to simplify their designs. Synthesis: Engineers

Expression (mathematics) (5,456 words) [view diff] no match in snippet view article

rewriting, a reduction strategy or rewriting strategy is a relation specifying a rewrite for each object or term, compatible with a given reduction relation

Algorithm (6,907 words) [view diff] no match in snippet view article find links to article

Medium is the message Regulation of algorithms Theory of computation Computability theory Computational complexity theory "Definition of ALGORITHM". Merriam-Webster

Proof of impossibility (3,915 words) [view diff] no match in snippet view article find links to article

later than Turing) was a short paper by Emil Post that discussed the reduction of an algorithm to a simple machine-like "method" very similar to Turing's

Second-order logic (4,502 words) [view diff] no match in snippet view article find links to article

formerly second-order quantifiers ranging over the second sort instead. This reduction can be attempted in a one-sorted theory by adding unary predicates that

Mathematical proof (4,780 words) [view diff] no match in snippet view article find links to article

contradiction, also known by the Latin phrase reductio ad absurdum (by reduction to the absurd), it is shown that if some statement is assumed true, a

Logicism (11,833 words) [view diff] no match in snippet view article find links to article

reduction of relation to the ordered pair of sets. Grattan-Guinness observes that in the second edition of Principia Russell ignored this reduction that

Hilary Putnam (8,912 words) [view diff] no match in snippet view article find links to article

previous research by Putnam, Julia Robinson and Martin Davis. In computability theory, Putnam investigated the structure of the ramified analytical hierarchy

Neurophilosophy (5,881 words) [view diff] no match in snippet view article find links to article

Church–Turing thesis, which formalized the mathematics underlying computability theory. The second group consisted of Warren McCulloch and Walter Pitts

Complexity class (10,382 words) [view diff] no match in snippet view article find links to article

breakdown into decidable and undecidable pertains more to the study of computability theory, but is useful for putting the complexity classes in perspective

Natural deduction (6,972 words) [view diff] no match in snippet view article find links to article

}}\wedge _{I}\end{aligned}}} These notions correspond exactly to β-reduction (beta reduction) and η-conversion (eta conversion) in the lambda calculus, using

Foundations of mathematics (6,910 words) [view diff] no match in snippet view article find links to article

smooth graph. At this point, the program of arithmetization of analysis (reduction of mathematical analysis to arithmetic and algebraic operations) advocated

Computer (14,125 words) [view diff] no match in snippet view article find links to article

organizations, clubs and societies of both a formal and informal nature. Computability theory Computer security Glossary of computer hardware terms History of

Satisfiability modulo theories (4,371 words) [view diff] no match in snippet view article find links to article

arithmetic (often implemented in SMT solvers via bit-blasting, i.e., reduction to bitvectors), strings, (co)-datatypes, sequences (used to model dynamic

Philosophy of mathematics (10,964 words) [view diff] no match in snippet view article find links to article

requirement of strong fragments of second-order logic to carry out his reduction, and because the statement of conservativity seems to require quantification

Church encoding (8,544 words) [view diff] no match in snippet view article find links to article

0} Calculating n − m {\displaystyle n-m} takes many beta reductions. Unless doing the reduction by hand, this doesn't matter that much, but it is preferable

History of mathematics (16,226 words) [view diff] no match in snippet view article find links to article

areas of mathematics were developed to deal with this: Alan Turing's computability theory; complexity theory; Derrick Henry Lehmer's use of ENIAC to further

Turing's proof (7,140 words) [view diff] no match in snippet view article find links to article

Hodges p. 125) — mainly because he had arrived simultaneously at a similar reduction of "algorithm" to primitive machine-like actions, so he took a personal

Constant-recursive sequence (5,040 words) [view diff] no match in snippet view article find links to article

constant-recursive sequence can also be investigated from the perspective of computability theory. To do so, the description of the sequence s n {\displaystyle s_{n}}

Glossary of artificial intelligence (29,481 words) [view diff] no match in snippet view article find links to article

divided into three major branches: automata theory and languages, computability theory, and computational complexity theory, which are linked by the question:

List of women in mathematics (23,282 words) [view diff] no match in snippet view article find links to article

educator Julia F. Knight, American specialist in model theory and computability theory Sarah Koch (born 1979), American complex analyst and complex dynamicist

January–March 2021 in science (13,101 words) [view diff] no match in snippet view article find links to article

January 2021). "Superintelligence Cannot be Contained: Lessons from Computability Theory". Journal of Artificial Intelligence Research. 70: 65–76. doi:10

Glossary of logic (30,237 words) [view diff] no match in snippet view article find links to article

logical and linguistic intuitions. busy beaver problem A problem in computability theory that seeks the Turing machine with the largest possible behavior