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Real number calculations and theorem proving
 Proceedings of the 18th International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2005, volume 3603 of Lecture Notes in Computer Science
, 2005
"... Abstract. Wouldn’t it be nice to be able to conveniently use ordinary real number expressions within proof assistants? In this paper we outline how this can be done within a theorem proving framework. First, we formally establish upper and lower bounds for trigonometric and transcendental functions. ..."
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Cited by 20 (5 self)
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Abstract. Wouldn’t it be nice to be able to conveniently use ordinary real number expressions within proof assistants? In this paper we outline how this can be done within a theorem proving framework. First, we formally establish upper and lower bounds for trigonometric and transcendental functions
Theorem Proving with the Real Numbers
, 1996
"... This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification ..."
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Cited by 119 (13 self)
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This thesis discusses the use of the real numbers in theorem proving. Typically, theorem provers only support a few `discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification
Fast probabilistic algorithms for verification of polynomial identities
 J. ACM
, 1980
"... ABSTRACT The starthng success of the RabmStrassenSolovay pnmahty algorithm, together with the intriguing foundattonal posstbthty that axtoms of randomness may constttute a useful fundamental source of mathemaucal truth independent of the standard axmmaUc structure of mathemaUcs, suggests a wgorous ..."
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Cited by 520 (1 self)
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and Sturm sequences are given. Probabilistlc calculatton in real anthmetlc, prewously considered by Davis, is justified ngorously, but only in a special case. Theorems of elementary geometry can be proved much more efficiently by the techmques presented than by any known arttficmlmtelhgence approach
Loopy belief propagation for approximate inference: An empirical study. In:
 Proceedings of Uncertainty in AI,
, 1999
"... Abstract Recently, researchers have demonstrated that "loopy belief propagation" the use of Pearl's polytree algorithm in a Bayesian network with loops can perform well in the context of errorcorrecting codes. The most dramatic instance of this is the near Shannonlimit performanc ..."
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Cited by 676 (15 self)
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in a more gen eral setting? We compare the marginals com puted using loopy propagation to the exact ones in four Bayesian network architectures, including two realworld networks: ALARM and QMR. We find that the loopy beliefs of ten converge and when they do, they give a good approximation
Fermat Last Theorem was Proved in 1991
, 1997
"... We found out a new method for proving Fermat last theorem (FL T) on the afternoon of October 25, 1991. We proved FLT at one stroke for all prime exponents p>3, It led to the discovery to calculate n = 15,21, 35, 105, ••.•••. To this date, no one disprove this proof Anyone can not deny it, becaus ..."
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We found out a new method for proving Fermat last theorem (FL T) on the afternoon of October 25, 1991. We proved FLT at one stroke for all prime exponents p>3, It led to the discovery to calculate n = 15,21, 35, 105, ••.•••. To this date, no one disprove this proof Anyone can not deny it
Theorem Proving in Higher Order Logics
, 2002
"... Syntax in Nuprl ::::::::::::::::::::::::::::::::::::::::::::: 23 Eli Barzilay, Stuart Allen DOVE: a Graphical Tool for the Analysis and Evaluation of Critical Systems :::::::::::::::::::::: 33 Tony Cant, Jim McCarthy, Brendan Mahony Formalising General Correctness ::::::::::::::::::::::::::::::: ..."
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:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 128 Konrad Slind The K Combinator as a Semantically TransparentTagging Mechanism:::::::::::::::::::::::::::: 139 Konrad Slind, Michael Norrish FCM 2002 Invited Talk Real Numbers in Real Applications ::::::::::::::::::::::::::::::::::::::::::::::::::::::::::: 146 John Harrison v vi FCM 2002
Proving RealValued Inequalities by Computation in Isabelle/HOL
"... In this thesis we present an automatic proof method on real valued formulas. It translates the formulas into interval arithmetic calculations on floating point numbers. The resulting formulas are then evaluated by utilizing the code generator. These computations are entirely verified in Isabelle/HOL ..."
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In this thesis we present an automatic proof method on real valued formulas. It translates the formulas into interval arithmetic calculations on floating point numbers. The resulting formulas are then evaluated by utilizing the code generator. These computations are entirely verified in Isabelle
An Incompleteness Theorem For Calculating The Future
"... : This paper proves that one can not build a computer which can, for any physical system, take the specification of that system's state as input and then correctly predict its future state before that future state actually occurs. Loosely speaking, this means that one can not build a physical c ..."
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: This paper proves that one can not build a computer which can, for any physical system, take the specification of that system's state as input and then correctly predict its future state before that future state actually occurs. Loosely speaking, this means that one can not build a physical
Distribution of prime numbers Fundamental Theorem
"... near x. Based on the density of the Gauss proposed regional distribution of prime numbers theorem. And regional distribution of prime numbers theorem proved easy to understand way. The fundamental theorem to obtain the distribution of prime numbers. Thus proving that a new prime number theorem. Ther ..."
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near x. Based on the density of the Gauss proposed regional distribution of prime numbers theorem. And regional distribution of prime numbers theorem proved easy to understand way. The fundamental theorem to obtain the distribution of prime numbers. Thus proving that a new prime number theorem
Verified Real Number Calculations: A Library for Interval Arithmetic
, 2007
"... Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly automated as well as interactive way. First, we formally est ..."
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Cited by 10 (1 self)
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Real number calculations on elementary functions are remarkably difficult to handle in mechanical proofs. In this paper, we show how these calculations can be performed within a theorem prover or proof assistant in a convenient and highly automated as well as interactive way. First, we formally
Results 1  10
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