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192
Avoiding Duplicate Proofs with the Foothold Refinement
 Annals of Mathematics and Artificial Intelligence
, 1994
"... Wos has identified the problem of recomputing redundant information in the general setting of automated reasoning. We consider this problem in the setting of logic programming where we are given a formula and a goal and asked to find the instances of the goal that follow from the formula. We can use ..."
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Cited by 2 (1 self)
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use a proof procedure to find the result. The procedure exhibits redundancy when it finds two results such that one either duplicates or is more specific than the other. We introduce the foothold format, a refinement of linear resolution that admits fewer duplicate proofs than Loveland's popular
Refined signbalance on 321 avoiding permutations
, 2003
"... Abstract. The number of even 321avoiding permutations of length n is equal to the number of odd ones if n is even, and exceeds it by the n−1 th Catalan number otherwise. We present an involution that proves a refinement 2 of this signbalance property respecting the length of the longest increasing ..."
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Cited by 4 (0 self)
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Abstract. The number of even 321avoiding permutations of length n is equal to the number of odd ones if n is even, and exceeds it by the n−1 th Catalan number otherwise. We present an involution that proves a refinement 2 of this signbalance property respecting the length of the longest
Refined SignBalance on 321Avoiding Permutations, preprint
, 2003
"... Abstract. The number of even 321avoiding permutations of length n is equal to the number of odd ones if n is even, and exceeds it by the n−1 th Catalan number otherwise. We present an involution that proves a refinement 2 of this signbalance property respecting the length of the longest increasing ..."
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Cited by 2 (1 self)
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Abstract. The number of even 321avoiding permutations of length n is equal to the number of odd ones if n is even, and exceeds it by the n−1 th Catalan number otherwise. We present an involution that proves a refinement 2 of this signbalance property respecting the length of the longest
Bijections for Refined Restricted Permutations
 J. Combin. Theory Ser. A
, 2004
"... We present a bijection between 321 and 132avoiding permutations that preserves the number of fixed points and the number of excedances. This gives a simple combinatorial proof of recent results of Robertson, Saracino and Zeilberger [8], and the first author [3]. We also show that our bijection pre ..."
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Cited by 25 (11 self)
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We present a bijection between 321 and 132avoiding permutations that preserves the number of fixed points and the number of excedances. This gives a simple combinatorial proof of recent results of Robertson, Saracino and Zeilberger [8], and the first author [3]. We also show that our bijection
A NOVEL APPROACH TO DETECT THE NEARDUPLICATES BY REFINING PROVENANCE MATRIX
"... Abstract: In this paper, the provenance matrix is refined to get more accuracy and efficiency in detecting nearduplicates by adding two more factors ‘How ’ and ‘Why ’ , as the performance of the web search depends on the search results having information without duplicates or redundancy. More redu ..."
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Abstract: In this paper, the provenance matrix is refined to get more accuracy and efficiency in detecting nearduplicates by adding two more factors ‘How ’ and ‘Why ’ , as the performance of the web search depends on the search results having information without duplicates or redundancy. More
Delaunay refinement for piecewise smooth complexes
 Proc. 18th Annu. ACMSIAM Sympos. Discrete Algorithms
, 2007
"... We present a Delaunay refinement algorithm for meshing a piecewise smooth complex in three dimensions. The algorithm protects edges with weighted points to avoid the difficulty posed by small angles between adjacent input elements. These weights are chosen to mimic the local feature size and to sati ..."
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Cited by 32 (5 self)
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We present a Delaunay refinement algorithm for meshing a piecewise smooth complex in three dimensions. The algorithm protects edges with weighted points to avoid the difficulty posed by small angles between adjacent input elements. These weights are chosen to mimic the local feature size
Extensible specifications for automatic reuse of specifications and proofs
 Software Engineering and Formal Methods
, 2012
"... Abstract. One way to reduce the cost of formally verifying a large program is to perform proofs over a specification of its behaviour, which its implementation refines. However, interesting programs must often satisfy multiple properties. Ideally, each property should be proved against the most abst ..."
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Cited by 5 (3 self)
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instantiations of it, avoiding unnecessary proof duplication. We explain how we applied this idea in the context of verifying confidentiality enforcement for the seL4 microkernel, saving us significant proof and code duplication. 1
PathFocused Duplication: rocedure for
"... The mating paradigm for automated theorem provers was proposed by Andrews to avoid some of the shortcomings in resolution. It facilitates automated deduction in higherorder and nonclassical logics. Moreover, there are procedures which translate back and forth between refutations by the mating meth ..."
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method and proofs in a natural deduction system. We describe a search procedure, called pathfocused duplication, for finding refutations by the mating method. This procedure, which is a complete strategy for the mating method, addresses two crucial issues (inadequately handled in current implementations
On the Constructive Content of Proofs
, 2003
"... This thesis aims at exploring the scopes and limits of techniques for extracting programs from proofs. We focus on constructive theories of inductive definitions and classical systems allowing choice principles. Special emphasis is put on optimizations that allow for the extraction of realistic prog ..."
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Cited by 14 (1 self)
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to this problem. First, we present a proof of Higman’s Lemma for an arbitrary alphabet in a theory of inductive definitions. This proof may be considered as a constructive counterpart to NashWilliams ’ minimalbadsequence proof. Secondly, using a refined Atranslation method, we directly transform the classical
Antimonotonybased Delay Avoidance for CHR
, 2004
"... We present an optimisation for Constraint Handling Rules (CHR) that reduces the amount of variables a constraint delays on. This optimisation reduces the overhead of delaying on variables as well as the needless reawakening of delayed constraint. A correctness proof of the optimisation based on the ..."
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Cited by 7 (5 self)
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on the refined operational semantics establishes the validity of the optimisation and sheds light on possible extensions as well as related optimisations. The delay avoidance optimisation shows good speedups for some programs and no noticable slowdown for others.
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