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Lightweight relevance filtering for machinegenerated resolution problems
 In ESCoR: Empirically Successful Computerized Reasoning
, 2006
"... Irrelevant clauses in resolution problems increase the search space, making it hard to find proofs in a reasonable time. Simple relevance filtering methods, based on counting function symbols in clauses, improve the success rate for a variety of automatic theorem provers and with various initial set ..."
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Cited by 47 (9 self)
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Irrelevant clauses in resolution problems increase the search space, making it hard to find proofs in a reasonable time. Simple relevance filtering methods, based on counting function symbols in clauses, improve the success rate for a variety of automatic theorem provers and with various initial settings. We have designed these techniques as part of a project to link automatic theorem provers to the interactive theorem prover Isabelle. They should be applicable to other situations where the resolution problems are produced mechanically and where completeness is less important than achieving a high success rate with limited processor time. 1
Formalizing an analytic proof of the prime number theorem
 Journal of Automated Reasoning
"... describe the computer formalization of a complexanalytic proof of the Prime Number Theorem (PNT), a classic result from number theory characterizing the asymptotic density of the primes. The formalization, conducted using the HOL Light theorem prover, proceeds from the most basic axioms for mathema ..."
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describe the computer formalization of a complexanalytic proof of the Prime Number Theorem (PNT), a classic result from number theory characterizing the asymptotic density of the primes. The formalization, conducted using the HOL Light theorem prover, proceeds from the most basic axioms for mathematics yet builds from that foundation to develop the necessary analytic machinery including Cauchy’s integral formula, so that we are able to formalize a direct, modern and elegant proof instead of the more involved ‘elementary ’ ErdösSelberg argument. As well as setting the work in context and describing the highlights of the formalization, we analyze the relationship between the formal proof and its informal counterpart and so attempt to derive some general lessons about the formalization of mathematics.
A Decision Procedure for Linear ”Big O” Equations
 J. Autom. Reason
"... Let F be the set of functions from an infinite set, S, to an ordered ring, R. For f, g, and h in F, the assertion f = g + O(h) means that for some constant C, f(x) − g(x)  ≤ Ch(x)  for every x in S. Let L be the firstorder language with variables ranging over such functions, symbols for 0,+, ..."
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Cited by 5 (0 self)
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Let F be the set of functions from an infinite set, S, to an ordered ring, R. For f, g, and h in F, the assertion f = g + O(h) means that for some constant C, f(x) − g(x)  ≤ Ch(x)  for every x in S. Let L be the firstorder language with variables ranging over such functions, symbols for 0,+, −,min,max, and absolute value, and a ternary relation f = g + O(h). We show that the set of quantifierfree formulas in this language that are valid in the intended class of interpretations is decidable, and does not depend on the underlying set, S, or the ordered ring, R. If R is a subfield of the real numbers, we can add a constant 1 function, as well as multiplication by constants from any computable subfield. We obtain further decidability results for certain situations in which one adds symbols denoting the elements of a fixed sequence of functions of strictly increasing rates of growth. 1
Contents 1 GCD: The Greatest Common Divisor 9
, 2008
"... 1.1 Specification of GCD on nats.................. 9 1.2 GCD on nat by Euclid’s algorithm............... 9 ..."
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1.1 Specification of GCD on nats.................. 9 1.2 GCD on nat by Euclid’s algorithm............... 9