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Correctness (computer science)
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In theoretical computer science, an algorithm is correct with respect to a specification if it behaves as specified. Best explored is functional correctnessKepler conjecture (2,700 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 accepted1992–93 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'sRice'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 andHOL (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. SystemsExperimental 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-basedBlakers–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 variantBohr–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 magnetizationNobuo 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; firstRealizability (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 provabilityCurry'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 notationDeduction 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;Arrow's impossibility theorem (5,620 words) [view diff] no match in snippet view article find links to article
Arrow's impossibility theorem is a key result in social choice showing that no ranked-choice voting rule can produce a logically coherent result when thereProgram 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 automationVerhoeff 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 decimalInvariant-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-trivialCoq (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 constructingThomas Callister Hales (962 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 "IntegratingBuckingham 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'sRepeating 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 sameQueue 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 coursesQuantum 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 givenPrimality 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 ofPrimality 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 ofSecurity 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 thisIsabelle (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 proofsPenrose–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 areVerification (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 parametersCAP theorem (933 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 clarifiedShadows of the Mind (1,768 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,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 importantFormal 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”Outline of computer science (1,042 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 cryptographyLogic 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 accelerateTrigger 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 eJapanese 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 allowedCovariance 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 principalRise time (3,448 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: theRigour (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 notPrices 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 sameQED 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. (openKenchū 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 allowedEdict 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 MaintenonMizar 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. WiedijkConjecture (3,046 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. FromRational 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. AnthonyButterfly 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 droppedMulti-party fair exchange protocol (238 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. FranklinHOL 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 SocietyPrinciple 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 versionNash-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)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 (FormalCayley–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 generalRyōan 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 allowedTime-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 thisIntegration 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 125Hand-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 oftenHaskell (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; ElphinstoneSeven Bridges of Königsberg (1,772 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)Markov's inequality (2,254 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.NP-completeness (3,612 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 notArthur 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." CayleyMcCarthy 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 proverAmicable 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, SergeiA 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 ofMathematical 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"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.;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 melodiesDirichlet 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–KrahnRevision theory (6,640 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 importantEquivalence (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-styleSphere packing (3,414 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 latticeGenerative 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 ofRichard 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; VolBackdoor (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 sourceBackdoor (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 sourceQuantum 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 negativeDivision by zero (5,653 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 thatLongest 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 pathPeyton 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 emerges99 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 ofOctonion (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"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, andSakugen 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 allowedOriginal 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 ofOn 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. GödelHam 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 areRC4 (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 securityPythagorean 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 sidesP 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 formalLagrange inversion theorem (2,936 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 doesFeit–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 2012Linear 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 JanuaryUDP-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 usingMany-worlds interpretation (8,298 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:0906.2718Koan (10,309 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 thanPACELC 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 theoremDirichlet 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 boundedIndependence 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. CertainlySylow 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"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 SocietyItô'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 variablesList 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 disproofNondeterministic finite automaton (4,495 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 articleTriple 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 ambiguitiesQuicksort (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 thereQuantum mind (8,586 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 BringsjordNotary 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 atGeneral 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 validityThe 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 rescindedQuaternion (12,662 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 –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 expressionTimeline of mathematics (7,710 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 FinallyIntuitionistic logic (7,646 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 ⊥Komar mass (2,245 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 ( 2 T a b − T g a b ) u a ξ b d V , {\displaystyle m=\intHistory of mathematics (15,999 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. CastelvecchiDharma transmission (7,981 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 thanPrime number theorem (8,185 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 NumberPierre-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 AlessandroQuantum key distribution (11,608 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 remappingLoop 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 languageGoodwen (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 theMaximum 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 reasoningMathematical 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, UniversityChebyshev's inequality (7,414 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 & GeuversGregory 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 environmentTimeline 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 believeAdministration 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 GermanyPredicate 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 operationalFoundations of geometry (10,902 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 ElementsHubertus 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 SpaceEducation 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 mayGilbert–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 linearSunflower (mathematics) (2,915 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 termLanguage-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 applicableCurry–Howard correspondence (6,172 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, itSeparation 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 enforcedOccupational 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 practiseMethods of computing square roots (11,773 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 geometricSzemerédi 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 workConvergence group (2,122 words) [view diff] exact match in snippet view article find links to article
{\displaystyle \partial G} is a uniform convergence action (see for a formal proof). Bowditch proved an important converse, thus obtaining a topologicalEnglish 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 caseEnvy-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 dataLaw 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 theoryCommunication complexity (6,775 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 ofLeon Henkin (10,309 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 toGlossary of computer science (23,798 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 rectangularList 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 GerardChurch 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 fromRoth'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)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 2002Tagged 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 thanGun 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 dealersHistory 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 archaeologicalCigéo (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