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searching for Formal proof 158 found (500 total)

Kepler conjecture (2,693 words) [view diff] exact match in snippet view article find links to article

completion of a formal proof of the Kepler conjecture using a combination of the Isabelle and HOL Light proof assistants. In 2017, the formal proof was accepted

Correctness (computer science) (660 words) [view diff] no match in snippet view article

In theoretical computer science, an algorithm is correct with respect to a specification if it behaves as specified. Best explored is functional correctness

1992–93 UEFA Champions League (815 words) [view diff] exact match in snippet view article find links to article

during the 1992–93 season. These investigations have not established any formal proof concerning alleged match-fixing in the Champions League. Therefore, Marseille's

Rice's theorem (1,686 words) [view diff] exact match in snippet view article find links to article

case, we would be able to solve the halting problem similarly. For the formal proof, algorithms are presumed to define partial functions over strings and

HOL (proof assistant) (725 words) [view diff] no match in snippet view article

HOL (Higher Order Logic) denotes a family of interactive theorem proving systems using similar (higher-order) logics and implementation strategies. Systems

Experimental mathematics (1,811 words) [view diff] exact match in snippet view article find links to article

Exploring a possible result to see if it is worth formal proof. Suggesting approaches for formal proof. Replacing lengthy hand derivations with computer-based

Bohr–Van Leeuwen theorem (1,564 words) [view diff] no match in snippet view article find links to article

The Bohr–Van Leeuwen theorem states that when statistical mechanics and classical mechanics are applied consistently, the thermal average of the magnetization

Blakers–Massey theorem (564 words) [view diff] exact match in snippet view article find links to article

definition was given by Charles Rezk in 2010. In 2013 a fairly short, fully formal proof using homotopy type theory as a mathematical foundation and an Agda variant

Nobuo Okishio (2,600 words) [view diff] case mismatch in snippet view article find links to article

propositions of dynamic movement of capitalistic economy. In the paper “A Formal Proof of Marx’s Two Theorems” he tried to prove Marx's two theorems; first

Realizability (1,006 words) [view diff] exact match in snippet view article find links to article

realizer, however, usually gives more information about the formula than a formal proof would directly provide. Beyond giving insight into intuitionistic provability

Arrow's impossibility theorem (4,293 words) [view diff] no match in snippet view article find links to article

Arrow's impossibility theorem is a key impossibility theorem in social choice theory, showing that no ranked voting rule can produce a logically coherent

Curry's paradox (2,427 words) [view diff] exact match in snippet view article find links to article

equivalent to (X → Y), then we can prove Y with a formal proof. One example of such a formal proof is as follows. For an explanation of the logic notation

Deduction theorem (3,088 words) [view diff] exact match in snippet view article find links to article

much shorter proofs than would be possible without it. In certain other formal proof systems the same conveniency is provided by an explicit inference rule;

Program synthesis (2,583 words) [view diff] exact match in snippet view article find links to article

to be constructed rather than given; however, both fields make use of formal proof techniques, and both comprise approaches of different degrees of automation

Verhoeff algorithm (1,504 words) [view diff] exact match in snippet view article find links to article

independently discovered by H. Peter Gumm in 1985, this time including a formal proof and an extension to any base. Verhoeff had the goal of finding a decimal

Invariant-based programming (266 words) [view diff] exact match in snippet view article find links to article

combined programming and specification language, connected to a powerful formal proof system, will generally be required for full verification of non-trivial

Coq (software) (1,698 words) [view diff] exact match in snippet view article

correctness proof in Coq was published in 2007. Feit–Thompson theorem: formal proof using Coq was completed in September 2012. In addition to constructing

Repeating decimal (7,270 words) [view diff] no match in snippet view article find links to article

A repeating decimal or recurring decimal is a decimal representation of a number whose digits are eventually periodic (that is, after some place, the same

Thomas Callister Hales (950 words) [view diff] exact match in snippet view article find links to article

give the Tarski Lectures in 2019. His three lectures were titled "A formal proof of the Kepler conjecture", "Formalizing mathematics", and "Integrating

Buckingham π theorem (5,461 words) [view diff] no match in snippet view article find links to article

In engineering, applied mathematics, and physics, the Buckingham π theorem is a key theorem in dimensional analysis. It is a formalisation of Rayleigh's

Queue automaton (768 words) [view diff] exact match in snippet view article find links to article

by simple transitions to the beginning and end symbols of the tape. A formal proof of this is often an exercise in theoretical computer science courses

CAP theorem (868 words) [view diff] exact match in snippet view article find links to article

Computing (PODC). In 2002, Seth Gilbert and Nancy Lynch of MIT published a formal proof of Brewer's conjecture, rendering it a theorem. In 2012, Brewer clarified

Quantum money (534 words) [view diff] exact match in snippet view article find links to article

cryptography. Wiesner's quantum money scheme was first published in 1983. A formal proof of security, using techniques from semidefinite programming, was given

Primality certificate (2,252 words) [view diff] exact match in snippet view article find links to article

computer science, a primality certificate or primality proof is a succinct, formal proof that a number is prime. Primality certificates allow the primality of

Security of cryptographic hash functions (1,950 words) [view diff] exact match in snippet view article find links to article

produce the hash. These are then believed to be hard to break, but no formal proof is given. Almost all hash functions in widespread use reside in this

Isabelle (proof assistant) (1,258 words) [view diff] exact match in snippet view article

lemma. Isar ("intelligible semi-automated reasoning") is Isabelle's formal proof language. It is inspired by the Mizar system. Isabelle allows proofs

Penrose–Lucas argument (2,364 words) [view diff] exact match in snippet view article find links to article

that can be simulated in a Turing machine. Penrose argued that while a formal proof system cannot prove its own consistency, Gödel-unprovable results are

Verification (spaceflight) (544 words) [view diff] exact match in snippet view article

Military) equipment" for non-safety relevant units. Qualification is the formal proof that the design meets all requirements of the specification and the parameters

Shadows of the Mind (1,781 words) [view diff] exact match in snippet view article find links to article

provable in the theory. The essence of Penrose's argument is that while a formal proof system cannot, because of the theorem, prove its own incompleteness,

Formal specification (1,261 words) [view diff] exact match in snippet view article find links to article

concrete problem domain, and such an abstraction step is not amenable to formal proof. However, it is possible to validate a specification by proving “challenge”

Mathematical practice (670 words) [view diff] exact match in snippet view article find links to article

relies on practicality (i.e., does it answer the question?) rather than formal proof. Mathematical teaching usually requires the use of several important

Logic simulation (832 words) [view diff] exact match in snippet view article find links to article

verification can also be explored as an alternative to simulation, although a formal proof is not always possible or convenient. A prospective way to accelerate

Trigger strategy (168 words) [view diff] exact match in snippet view article find links to article

A non-cooperative equilibrium for supergames, Review of Economic Studies 38, 1–12. (The first formal proof of the Folk theorem (game theory)). v t e

Outline of computer science (1,053 words) [view diff] exact match in snippet view article find links to article

other ways of modeling logical queries; the uses and limitations of formal proof methods Number theory – Theory of the integers. Used in cryptography

Covariance matrix (5,418 words) [view diff] exact match in snippet view article find links to article

data in a compact way[citation needed] (see Rayleigh quotient for a formal proof and additional properties of covariance matrices). This is called principal

Japanese missions to Ming China (699 words) [view diff] exact match in snippet view article find links to article

100 such tallies were conveyed to Japan in 1404. Only those with this formal proof of Imperial permission represented by the document were officially allowed

Rise time (3,241 words) [view diff] exact match in snippet view article find links to article

rise time is proportional to the network time constant τ = L⁄R. The formal proof of this assertion proceed exactly as shown in the previous section: the

Rigour (1,629 words) [view diff] exact match in snippet view article find links to article

language. In this sense, written mathematical discourse is a prototype of formal proof. Often, a written proof is accepted as rigorous although it might not

Prices of production (15,152 words) [view diff] exact match in snippet view article find links to article

itself cannot contain any formal proof of a necessary quantitative relationship between values and prices, nor a formal proof that capitals of the same

Kenchū Keimitsu (588 words) [view diff] exact match in snippet view article find links to article

were conveyed to Japan by Kenchū Keimitsu in 1404. Only those with this formal proof of Imperial permission represented by the document were officially allowed

Edict of Fontainebleau (1,451 words) [view diff] exact match in snippet view article find links to article

thought to have urged Louis to revoke Henry IV's edict. There is no formal proof of that, and such views have now been challenged. Madame de Maintenon

Mizar system (1,169 words) [view diff] case mismatch in snippet view article find links to article

doi:10.1007/s12046-009-0001-5. hdl:2066/75958. Wiedijk, Freek (2008). "Formal Proof--Getting Started" (PDF). Notices of the AMS. 55 (11): 1408–1414. Wiedijk

QED manifesto (567 words) [view diff] case mismatch in snippet view article find links to article

the Royal Society 363 no. 1835, 2351–2375, 2005 "A Special Issue on Formal Proof". Notices of the American Mathematical Society. December 2008. (open

Conjecture (3,045 words) [view diff] case mismatch in snippet view article find links to article

Records. Guinness Publishing Ltd. 1995. Georges Gonthier (December 2008). "Formal Proof—The Four-Color Theorem". Notices of the AMS. 55 (11): 1382–1393. From

Rational number (3,494 words) [view diff] exact match in snippet view article find links to article

countable densely ordered sets without endpoints are isomorphic - a formal proof with KIV (PDF) (Technical report). Retrieved 17 August 2021. Anthony

Butterfly theorem (660 words) [view diff] exact match in snippet view article find links to article

chord PQ at X and Y correspondingly. Then M is the midpoint of XY. A formal proof of the theorem is as follows: Let the perpendiculars XX′ and XX″ be dropped

Multi-party fair exchange protocol (229 words) [view diff] case mismatch in snippet view article find links to article

Ritter, Eike. "Analysis of a Multi-Party Fair Exchange Protocol and Formal Proof of Correctness in the Strand Space model". Financial Crypto. 2005. Franklin

Java virtual machine (3,411 words) [view diff] exact match in snippet view article find links to article

system, clipboard, execute external pieces of software, or network. Formal proof of bytecode verifiers have been done by the Javacard industry (Formal

Multi-party fair exchange protocol (229 words) [view diff] case mismatch in snippet view article find links to article

Ritter, Eike. "Analysis of a Multi-Party Fair Exchange Protocol and Formal Proof of Correctness in the Strand Space model". Financial Crypto. 2005. Franklin

HOL Light (152 words) [view diff] case mismatch in snippet view article find links to article

University Press, ISBN 9780521356534 Freek Wiedijk (December 2008), "Formal Proof — Getting Started" (PDF), Notices of the American Mathematical Society

Nash-Williams theorem (463 words) [view diff] exact match in snippet view article find links to article

ISSN 1435-5914. S2CID 206791653. Paulson, Lawrence C. The Nash-Williams partition theorem (Formal proof development in Isabelle/HOL, Archive of Formal Proofs)

Principle of explosion (1,162 words) [view diff] exact match in snippet view article find links to article

are both true, then it logically follows that Q is true. Below is a formal proof of the principle using symbolic logic. This is just the symbolic version

Cayley–Hamilton theorem (11,169 words) [view diff] exact match in snippet view article find links to article

stated “..., I have not thought it necessary to undertake the labor of a formal proof of the theorem in the general case of a matrix of any degree”. The general

Ryōan Keigo (376 words) [view diff] exact match in snippet view article find links to article

100 such tallies were conveyed to Japan in 1404. Only those with this formal proof of Imperial permission represented by the document were officially allowed

Markov's inequality (2,097 words) [view diff] exact match in snippet view article find links to article

Ross, Kevin. 5.4 Probability inequalitlies | An Introduction to Probability and Simulation. The formal proof of Markov's inequality in the Mizar system.

Time-invariant system (1,355 words) [view diff] exact match in snippet view article find links to article

Shift-Invariant System as a function of time, t, System A is not. A more formal proof of why systems A and B above differ is now presented. To perform this

Integration by substitution (3,311 words) [view diff] exact match in snippet view article find links to article

variables by Mikhail Ostrogradsky in 1836, it resisted a fully rigorous formal proof for a surprisingly long time, and was first satisfactorily resolved 125

Seven Bridges of Königsberg (1,767 words) [view diff] case mismatch in snippet view article find links to article

Graph Problem Li, Wenda. The Königsberg Bridge Problem and the Friendship Theorem (Formal Proof Development in Isabelle/HOL, Archive of Formal Proofs)

Hand-waving (2,339 words) [view diff] exact match in snippet view article find links to article

mathematics plays a major role, hand-waving refers to either absence of formal proof or methods that do not meet mathematical rigor. In practice, it often

Haskell (4,530 words) [view diff] exact match in snippet view article find links to article

Functional Programming Workshop Report" (PDF). Retrieved 10 June 2022. A formal proof of functional correctness was completed in 2009. Klein, Gerwin; Elphinstone

NP-completeness (3,618 words) [view diff] exact match in snippet view article find links to article

Mathematics Institute is offering a US$1 million reward to anyone who has a formal proof that P=NP or that P≠NP. The existence of NP-complete problems is not

Arthur Cayley (2,024 words) [view diff] exact match in snippet view article find links to article

… but I have not thought it necessary to undertake the labour of a formal proof of the theorem in the general case of a matrix of any degree." Cayley

Revision theory (6,443 words) [view diff] exact match in snippet view article find links to article

Revision theory provides formal semantics for defined expressions, and formal proof systems study the logic of circular expressions. Definitions are important

McCarthy 91 function (1,260 words) [view diff] exact match in snippet view article find links to article

91 function to include additional parameters. John Cowles developed a formal proof that Knuth's generalized function was total, using the ACL2 theorem prover

Amicable numbers (2,308 words) [view diff] exact match in snippet view article find links to article

2020-06-09. Koutsoukou-Argyraki, Angeliki (4 August 2020). "Amicable Numbers (Formal proof development in Isabelle/HOL, Archive of Formal Proofs)". Chernykh, Sergei

A Guide to the Classification Theorem for Compact Surfaces (644 words) [view diff] exact match in snippet view article find links to article

presentation of the topological tools needed to prove the result, and a formal proof of the classification. Other topics in topology discussed as part of

Guillaume Franc (854 words) [view diff] exact match in snippet view article find links to article

January 1571, which remains the last trace of him. Although there is no formal proof, it is generally accepted that Franc was responsible for the first melodies

Clark–Wilson model (1,122 words) [view diff] exact match in snippet view article find links to article

The semantic verification is deferred to a separate model and general formal proof tools. Confused deputy problem Clark, David D.; and Wilson, David R.;

Backdoor (computing) (4,199 words) [view diff] exact match in snippet view article

stage-1 compilers must then result in two identical stage-2 compilers. A formal proof is given that the latter comparison guarantees that the purported source

Dirichlet eigenvalue (1,071 words) [view diff] exact match in snippet view article find links to article

of the force of pressure should be also zero. However, there exists a formal proof, which does not refer to the analogy with the physical system. Rayleigh–Faber–Krahn

Mathematical maturity (632 words) [view diff] exact match in snippet view article find links to article

of a mathematical argument that can subsequently be converted into a formal proof. The emphasis is now on applications, intuition, and the “big picture"

Generative Modelling Language (914 words) [view diff] exact match in snippet view article find links to article

The interactive applet conveys a good intuition of the idea behind the formal proof. Procedural generation OpenSCAD Michael Leyton. A Generative Theory of

Equivalence (formal languages) (692 words) [view diff] exact match in snippet view article

CSLI publications. "Yoshinaga, N., Miyao Y., and Tsujii, J. 2002. A formal proof of strong equivalence for a grammar conversion from LTAG to HPSG-style

Sphere packing (3,328 words) [view diff] exact match in snippet view article find links to article

Hales' proof. On 10 August 2014, Hales announced the completion of a formal proof using automated proof checking, removing any doubt. Some other lattice

Richard Bornat (520 words) [view diff] case mismatch in snippet view article find links to article

Press; pp. 225–255. Richard Bornat and Bernard Sufrin;1999; Animating Formal Proof at the Surface: The {Jape} Proof Calculator; The Computer Journal; Vol

Form W-2 (1,720 words) [view diff] exact match in snippet view article find links to article

track an employee's tax liability, and the form has come to be seen as a formal proof of income. The Social Security Administration, court proceedings, and

Division by zero (5,631 words) [view diff] exact match in snippet view article find links to article

equivalence classes are then defined to be the rational numbers. It is in the formal proof that this relation is an equivalence relation that the requirement that

Sakugen Shūryō (546 words) [view diff] exact match in snippet view article find links to article

100 such tallies were conveyed to Japan in 1404. Only those with this formal proof of Imperial permission represented by the document were officially allowed

Longest path problem (2,662 words) [view diff] exact match in snippet view article find links to article

path in a tree was proposed by Edsger Dijkstra around 1960, while a formal proof of this algorithm was published in 2002. Furthermore, a longest path

Peyton Young (2,563 words) [view diff] exact match in snippet view article find links to article

played virtually all the time, as time goes to infinity. It also yields a formal proof of Thomas Schelling's (1971) result that residential segregation emerges

Quantum indeterminacy (2,454 words) [view diff] exact match in snippet view article find links to article

formalism he was proposing. However, according to Bell, von Neumann's formal proof did not justify his informal conclusion. A definitive but partial negative

Octonion (4,419 words) [view diff] exact match in snippet view article find links to article

Stevin, 34: 106–125, MR 0130283 Koutsoukou-Argyraki, Angeliki. Octonions (Formal proof development in Isabelle/HOL, Archive of Formal Proofs) "Cayley numbers"

99 Points of Intersection (500 words) [view diff] exact match in snippet view article find links to article

interactive geometry software and in a geometry course focused on the formal proof of geometry propositions. He adds that the book itself is a proof of

Koan (8,222 words) [view diff] no match in snippet view article find links to article

old cases will he recognize the latter as a dharma heir and give him formal "proof of transmission" (J. inka shomei). Thus, in reality, a lot more than

Original proof of Gödel's completeness theorem (4,798 words) [view diff] exact match in snippet view article find links to article

inference, as in Gödel's paper, or it may be proved by considering the formal proof of ¬ Φ {\displaystyle \neg \Phi } , replacing in it all occurrences of

On Formally Undecidable Propositions of Principia Mathematica and Related Systems (1,354 words) [view diff] exact match in snippet view article find links to article

method now known as Gödel numbering. In this method, each sentence and formal proof in first-order arithmetic is assigned a particular natural number. Gödel

Pythagorean theorem (12,566 words) [view diff] exact match in snippet view article find links to article

having the same area as one of the two squares on the legs. For the formal proof, we require four elementary lemmata: If two triangles have two sides

Ham sandwich theorem (2,453 words) [view diff] exact match in snippet view article find links to article

the positive side of π(p)). This function f is continuous (which, in a formal proof, would need some justification). By the Borsuk–Ulam theorem, there are

P versus NP problem (7,720 words) [view diff] exact match in snippet view article find links to article

... it would transform mathematics by allowing a computer to find a formal proof of any theorem which has a proof of a reasonable length, since formal

RC4 (5,058 words) [view diff] exact match in snippet view article find links to article

the next 256 rounds. This conjecture was put to rest in 2004 with a formal proof given by Souradyuti Paul and Bart Preneel. In 2013, a group of security

Linear programming (6,567 words) [view diff] exact match in snippet view article find links to article

he had been working in game theory was equivalent. Dantzig provided formal proof in an unpublished report "A Theorem on Linear Inequalities" on January

Lagrange inversion theorem (2,833 words) [view diff] exact match in snippet view article find links to article

really needed is some property of the formal residue, and a more direct formal proof is available. If f is a formal power series, then the above formula does

Feit–Thompson theorem (2,854 words) [view diff] exact match in snippet view article find links to article

the original proof, but is written in a more leisurely style. A fully formal proof, checked with the Coq proof assistant, was announced in September 2012

Sylow theorems (4,390 words) [view diff] exact match in snippet view article find links to article

Zbl 0829.01011. Kammüller, Florian; Paulson, Lawrence C. (1999). "A formal proof of Sylow's theorem. An experiment in abstract algebra with Isabelle HOL"

UDP-based Data Transfer Protocol (1,468 words) [view diff] exact match in snippet view article find links to article

scientific communities. To analyze the security mechanisms, they carry out a formal proof of correctness to assist them in determining their applicability by using

Four color theorem (6,275 words) [view diff] case mismatch in snippet view article find links to article

archived (PDF) from the original on 2017-09-08 Gonthier, Georges (2008), "Formal Proof—The Four-Color Theorem" (PDF), Notices of the American Mathematical Society

Dirichlet distribution (6,539 words) [view diff] exact match in snippet view article find links to article

colored balls in the urn will be distributed as Dir(α1,...,αK). For a formal proof, note that the proportions of the different colored balls form a bounded

Quicksort (9,985 words) [view diff] exact match in snippet view article find links to article

divide-and-conquer recurrences tells us that T(n) = O(n log n). The outline of a formal proof of the O(n log n) expected time complexity follows. Assume that there

Independence of premise (1,257 words) [view diff] exact match in snippet view article find links to article

truth value. More specifically, θ shall express that x is the index of a formal proof of some mathematical conjecture whose provability is not known. Certainly

Many-worlds interpretation (8,297 words) [view diff] exact match in snippet view article find links to article

probability rule". arXiv:quant-ph/0312157. Wallace, David (2009). "A formal proof of the Born rule from decision-theoretic assumptions". arXiv:0906.2718

Itô's lemma (5,299 words) [view diff] exact match in snippet view article find links to article

problem, we can determine the mean and higher moments of the process. A formal proof of the lemma relies on taking the limit of a sequence of random variables

PACELC theorem (983 words) [view diff] exact match in snippet view article find links to article

University. Original blog post that first described PACELC "Proving PACELC", by Wojciech Golab, University of Waterloo Formal proof of the PACELC theorem

List of unsolved problems in mathematics (19,531 words) [view diff] exact match in snippet view article find links to article

Problems Scottish Book An aperiodic monotile has been discovered and the formal proof is awaiting publication. A preprint of the proof is available. A disproof

Nondeterministic finite automaton (4,498 words) [view diff] exact match in snippet view article find links to article

lead to an exponential rise in the number of necessary states. For a formal proof of the powerset construction, please see the Powerset construction article

Triple product rule (1,584 words) [view diff] exact match in snippet view article find links to article

and the nonzero value of partial derivatives and their reciprocals. A formal proof based on mathematical analysis would eliminate these potential ambiguities

Notary public (New York) (1,259 words) [view diff] exact match in snippet view article

the testator and the two (subscribing) witnesses, which will serve as formal proof and testimony of the proper will execution in the probate process at

Komar mass (1,947 words) [view diff] exact match in snippet view article find links to article

present the applicable result from (Wald, 1984 eq 11.2.10) without a formal proof. m=∫V(2Tab−Tgab)uaξbdV,{\displaystyle m=\int _{V}\left(2T_{ab}-Tg_{ab}\right)u^{a}\xi

The Harmon (4,209 words) [view diff] exact match in snippet view article find links to article

again in August 2013, after reviewing the latest test data from MGM. A formal proof of loss for the building was filed shortly thereafter. Gonzalez rescinded

General relativity (22,670 words) [view diff] exact match in snippet view article find links to article

behind a horizon, and thus invisible to all distant observers. While no formal proof yet exists, numerical simulations offer supporting evidence of its validity

Quantum mind (8,593 words) [view diff] exact match in snippet view article find links to article

mathematicians. Penrose took this to mean that human mathematicians are not formal proof systems and not running a computable algorithm. According to Bringsjord

Intuitionistic logic (7,619 words) [view diff] exact match in snippet view article find links to article

\to \psi ){\big )}\to {\big (}\phi \to (\chi \to \psi ){\big )}} . A formal proof of the latter using the Hilbert system is given on that page. With ⊥

Noether's theorem (10,847 words) [view diff] exact match in snippet view article find links to article

physical quantity is usually expressed as a continuity equation. The formal proof of the theorem utilizes the condition of invariance to derive an expression

Orchestrated objective reduction (5,312 words) [view diff] exact match in snippet view article find links to article

this disparity to mean that human mathematicians are not describable as formal proof systems, and are therefore running a non-computable algorithm. If correct

Timeline of mathematics (7,723 words) [view diff] exact match in snippet view article find links to article

400-year-old fruit-stacking problem, 12 August 2014; New Scientist. A formal proof of the Kepler conjecture, arXiv. Solved: 400-Year-Old Maths Theory Finally

Quaternion (12,730 words) [view diff] exact match in snippet view article find links to article

to Quaternions at Wikimedia Commons Paulson, Lawrence C. Quaternions (Formal proof development in Isabelle/HOL, Archive of Formal Proofs) Quaternions –

History of mathematics (15,998 words) [view diff] case mismatch in snippet view article find links to article

1090/S0002-9904-1902-00923-3. ISSN 0002-9904. Gonthier, Georges (December 2008). "Formal Proof—The Four-Color Theorem" (PDF). Notices of the AMS. 55 (11): 1382. Castelvecchi

Prime number theorem (8,178 words) [view diff] exact match in snippet view article find links to article

Oliveira e Silva Eberl, Manuel and Paulson, L. C. The Prime Number Theorem (Formal proof development in Isabelle/HOL, Archive of Formal Proofs) The Prime Number

Pierre-Simon Laplace (13,186 words) [view diff] exact match in snippet view article find links to article

verbal argument is so rigorous that it can easily be converted into a formal proof. Laplace died in Paris on 5 March 1827, which was the same day Alessandro

Quantum key distribution (11,613 words) [view diff] exact match in snippet view article find links to article

similarly be defeated by modifying the implementation, though there is no formal proof. Several other attacks including faked-state attacks, phase remapping

Dharma transmission (7,979 words) [view diff] no match in snippet view article find links to article

old cases will he recognize the latter as a dharma heir and give him formal "proof of transmission" (J. inka shomei). Thus, in reality, a lot more than

Loop variant (1,537 words) [view diff] exact match in snippet view article find links to article

be proven to do so; thus it is unavoidable that any requirement for a formal proof of termination must reduce the expressive power of a programming language

Goodwen (1,061 words) [view diff] exact match in snippet view article find links to article

that Goodwen had stolen his music without consent. The performer has no formal proof other than a recording of the song "A Glance at the Present from the

Mathematical economics (13,620 words) [view diff] case mismatch in snippet view article find links to article

original on April 17, 2008. Retrieved 2008-09-28. Dixon, Robert. "A Formal Proof of Walras Law". Walras Law Guide. Department of Economics, University

Maximum principle (3,699 words) [view diff] exact match in snippet view article find links to article

the hypothetical maximum point. This phenomenon is important in the formal proof of the classical weak maximum principle. However, the above reasoning

Chebyshev's inequality (7,350 words) [view diff] exact match in snippet view article find links to article

Chebyshev's inequality. "Chebyshev inequality in probability theory", Encyclopedia of Mathematics, EMS Press, 2001 [1994] Formal proof in the Mizar system.

Lambda cube (3,102 words) [view diff] case mismatch in snippet view article find links to article

S2CID 44757552. Nederpelt, Rob; Geuvers, Herman (2014). Type Theory and Formal Proof. Cambridge University Press. p. 69. ISBN 9781107036505. Nederpelt & Geuvers

Gregory Dudek (1,273 words) [view diff] exact match in snippet view article find links to article

so-called "trash can robots". With his colleagues he produced the first formal proof of the complexity of global robot localization in a metric environment

Predicate transformer semantics (3,380 words) [view diff] exact match in snippet view article find links to article

S2CID 13214445. Tutorial on Hoare Logic: a Coq library, giving a simple but formal proof that Hoare logic is sound and complete with respect to an operational

Timeline of scientific discoveries (10,204 words) [view diff] exact match in snippet view article find links to article

Greek mathematician Euclid in the Elements describes a primitive form of formal proof and axiomatic systems. However, modern mathematicians generally believe

Foundations of geometry (10,876 words) [view diff] exact match in snippet view article find links to article

secondary school as the first axiomatic system and the first examples of formal proof. It goes on to the solid geometry of three dimensions. Much of the Elements

Administration of Justice (Scotland) Act 1933 (969 words) [view diff] exact match in snippet view article

criminal trials on indictment were given a right to admit documents without formal proof by the other side; by agreement between the prosecution and defence,

Carl Diem (3,057 words) [view diff] exact match in snippet view article find links to article

Two days later, the students recanted, and admitted that there was no "formal proof" of the allegation. In the 1990s, a public debate erupted in Germany

Education in Germany (15,479 words) [view diff] exact match in snippet view article find links to article

students can qualify for university entrance if they present additional formal proof that they will be able to keep up with their fellow students. This may

Hubertus Strughold (3,111 words) [view diff] exact match in snippet view article find links to article

notable contributions to the American space program and the lack of any formal proof of his direct involvement in war crimes. Known as The Father of Space

Gilbert–Varshamov bound for linear codes (1,481 words) [view diff] exact match in snippet view article find links to article

probabilistic method, there exists the linear code satisfying the theorem. Formal proof: By using the probabilistic method, to show that there exists a linear

Sunflower (mathematics) (2,888 words) [view diff] exact match in snippet view article

(personal blog) Thiemann, René. The Sunflower Lemma of Erdős and Rado (Formal proof development in Isabelle/HOL, Archive of Formal Proofs) The original term

Language-based security (2,108 words) [view diff] exact match in snippet view article find links to article

certifying compiler is the Touchstone compiler, that provides a PCC formal proof of type- and memory safety for programs implemented in Java. TAL is applicable

Curry–Howard correspondence (6,197 words) [view diff] exact match in snippet view article find links to article

formulation, the Curry–Howard correspondence is a correspondence between formal proof calculi and type systems for models of computation. In particular, it

Separation kernel (858 words) [view diff] exact match in snippet view article find links to article

which the conformant product is integrated". The seL4 microkernel has a formal proof of concept that it can be configured as a separation kernel. The enforced

Occupational licensing (5,005 words) [view diff] exact match in snippet view article find links to article

recently proposed that they should all be legally required to produce formal proof, every five years, that they are upgrading their standard of practise

Methods of computing square roots (11,670 words) [view diff] exact match in snippet view article find links to article

reasonably be expected to provide a better approximation (though the formal proof of that assertion depends on the inequality of arithmetic and geometric

Szemerédi regularity lemma (6,159 words) [view diff] exact match in snippet view article find links to article

Koutsoukou-Argyraki, Angeliki; Paulson, Lawrence C. Szemerédi's regularity lemma (Formal proof development in Isabelle/HOL, Archive of Formal Proofs)

PL/C (4,264 words) [view diff] exact match in snippet view article find links to article

1975, that was known as PL/CV, which supplied some language support for formal proof of correctness and which ran as a separate verifier step. The PL/CV work

Convergence group (2,065 words) [view diff] exact match in snippet view article find links to article

∂G{\displaystyle \partial G} is a uniform convergence action (see for a formal proof). Bowditch proved an important converse, thus obtaining a topological

English contract law (28,902 words) [view diff] exact match in snippet view article find links to article

simple breach of a covenant (a solemn promise) had required production of formal proof of the agreement with a seal. However, in The Humber Ferryman's case

Envy-graph procedure (3,296 words) [view diff] exact match in snippet view article find links to article

agent is selected such that agent-item utility is maximized. There is no formal proof to the properties of this algorithm, but it fares well on realistic data

Communication complexity (6,563 words) [view diff] exact match in snippet view article find links to article

set is small enough that the choice can be communicated efficiently. A formal proof follows. Consider some random protocol P with a maximum error rate of

Leon Henkin (10,313 words) [view diff] exact match in snippet view article find links to article

noted that the aim of the paper was to show that every tautology had a formal proof in the system of axioms presented, and I expended my utmost effort to

Glossary of computer science (23,790 words) [view diff] exact match in snippet view article find links to article

of the expressive power of formal systems and the deductive power of formal proof systems. matrix In mathematics, a matrix, (plural matrices), is a rectangular

List of Dutch discoveries (10,146 words) [view diff] exact match in snippet view article find links to article

of galaxies and found their movements similarly perplexing. The first formal proof of the existence of an atmosphere around Titan came in 1944, when Gerard

Church of Saint-Sulpice, Jumet (2,670 words) [view diff] exact match in snippet view article find links to article

1753. The steeple was designed to hold three bells, however there is no formal proof of the existence of the third bell. On the east side, a first bell from

Roth's theorem on arithmetic progressions (4,444 words) [view diff] exact match in snippet view article find links to article

Koutsoukou-Argyraki, Angeliki; Paulson, Lawrence C. Roth's Theorem on Arithmetic Progressions (Formal proof development in Isabelle/HOL, Archive of Formal Proofs)

Law of thought (11,577 words) [view diff] no match in snippet view article find links to article

be "founded" in two ways, first as a "model theory", or second by a formal "proof" or "axiomatic theory"; "the two formulations, that of model theory

Theory of conjoint measurement (6,030 words) [view diff] exact match in snippet view article find links to article

choice behaviour such as the Allais Paradox. David Krantz wrote the formal proof to prospect theory using the theory of conjoint measurement. In 2002

Tagged Deterministic Finite Automaton (4,605 words) [view diff] exact match in snippet view article find links to article

POSIX disambiguation algorithm by Okui and Suzuki to TDFA. They gave a formal proof of correctness of the new algorithm and showed that it is faster than

Gun laws in Poland (15,547 words) [view diff] exact match in snippet view article find links to article

their modern replicas. The latter case is often used domestically as a formal proof of legal possession needed to buy black powder from local licensed dealers

History of the Cyclades (16,309 words) [view diff] exact match in snippet view article find links to article

House) or at Phylakopi might be the palaces of foreign governors, but no formal proof exists that could back up this hypothesis. Likewise, too few archaeological

Cigéo (8,599 words) [view diff] exact match in snippet view article find links to article

Andra has had to retreat little by little from attempting to produce a formal proof of the absolute safety of disposal to instead presenting a body of arguments