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

Abstract. The number of even 321-avoiding 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 sign-balance property respecting the length of the longest

Abstract. The number of even 321-avoiding 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 sign-balance property respecting the length of the longest

We present a bijection between 321- and 132-avoiding 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

Abstract:- In this paper, the provenance matrix is refined to get more accuracy and efficiency in detecting near-duplicates 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

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

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

method and proofs in a natural deduction system. We describe a search procedure, called path-focused 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

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 Nash-Williams ’ minimal-bad-sequence proof. Secondly, using a refined A-translation method, we directly transform the classical

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.