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A Graphbased Strategy for the Selection of Hypotheses
"... In previous works on verifying C programs by deductive approaches based on SMT provers, we proposed the heuristic of separation analysis to handle the most difficult problems. Nevertheless, this heuristic is not sufficient when applied on industrial C programs: it remains some Verification Condition ..."
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In previous works on verifying C programs by deductive approaches based on SMT provers, we proposed the heuristic of separation analysis to handle the most difficult problems. Nevertheless, this heuristic is not sufficient when applied on industrial C programs: it remains some Verification Conditions (VCs) that cannot be decided by any SMT prover, mainly due to their size. This work presents a strategy to select relevant hypotheses in each VC. The relevance of an hypothesis is the combination of two separated dependency analysis obtained by some graph traversals. The approach is applied on a benchmark issued from an industrial program verification.
Graphbased Reduction of Program Verification Conditions
 AUTOMATED FORMAL METHODS (AFM'09), COLOCATED WITH CAV'09 (2009) 4047
, 2009
"... Increasing the automaticity of proofs in deductive verification of C programs is a challenging task. When applied to industrial C programs known heuristics to generate simpler verification conditions are not efficient enough. This is mainly due to their size and a high number of irrelevant hypothese ..."
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Increasing the automaticity of proofs in deductive verification of C programs is a challenging task. When applied to industrial C programs known heuristics to generate simpler verification conditions are not efficient enough. This is mainly due to their size and a high number of irrelevant hypotheses. This work presents a strategy to reduce program verification conditions by selecting their relevant hypotheses. The relevance of a hypothesis is determined by the combination of a syntactic analysis and two graph traversals. The first graph is labeled by constants and the second one by the predicates in the axioms. The approach is applied on a benchmark arising in industrial program verification.
The strategy of Cramming
 Preprint ANL/MCSP8980801, Mathematics and Computer Science Division, Argonne National Laboratory, Argonne, IL, 2001. Mathematics and Computer Science Division Argonne National Laboratory Argonne, IL 60439
"... The problem in focus in this article concerns proof shortening, and featured prominently is a strategy, cramming, for addressing that problem. The literature shows that this problem was indeed of interest to some of the masters of logic, masters that included C. A. Meredith, A. Prior, and I. Thomas ..."
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The problem in focus in this article concerns proof shortening, and featured prominently is a strategy, cramming, for addressing that problem. The literature shows that this problem was indeed of interest to some of the masters of logic, masters that included C. A. Meredith, A. Prior, and I. Thomas. The problem of proof shortening (as well as other aspects of simplication) is also germane to the recent discovery by R. Thiele of Hilbert's twentyfourth problem. The cramming strategy (introduced in this article) was formulated to seek shorter proofs, starting with some known proof, usually the shortest oered by the literature. The most impressive success with the use of this strategy concerns an abridgment of the MeredithPrior abridging of the Lukasiewicz proof for his shortest single axiom for the implicational fragment of twovalued sentential (or propositional) calculus. 1 Perspective and Wellspring In this article, the cramming strategy is introduced, a strategy designed to aid the researcher in nding shorter proofs than those in hand or those oered by the literature. The events that led to its formulation merit review. In the early 1990s, my colleague William McCune and I embarked on a study designed to produce a proof relying solely on condensed detachment showing that the fth of Lukasiewicz's ve axioms (which he conjectured to suce for innitevalued sentential calculus) is in fact dependent on the other four [Meredith1958]. (The conjecture was proved
The Use of Lemmas for Solving Hard Automated (May 2005)
, 2005
"... Thesis supervised by Professor Geoff Sutcliffe. No. of pages in text. (61) Using lemmas has been proved to be an effective approach to assisting ATP sytems to solve hard problems. Useful lemmas can provide valuable guidance in the proof search, and help construct the proof by filling in intermediate ..."
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Thesis supervised by Professor Geoff Sutcliffe. No. of pages in text. (61) Using lemmas has been proved to be an effective approach to assisting ATP sytems to solve hard problems. Useful lemmas can provide valuable guidance in the proof search, and help construct the proof by filling in intermediate steps. However, the formulae supplied to an ATP system as lemmas are not all necessarily useful. Unuseful lemmas act as noise, disturbing the search for the proof. It is therefore necessary to develop lemma management techniques that identify useful lemmas, and help an ATP system to use the useful lemmas to its advantage. This thesis presents three lemma management techniques. Their implementaton is reported. The potential of these techniques is illustrated with example problems. It has been shown that, with these three lemma management techniques, the problemsolving ability of an ATP system is improved. A recommendation for future work is enclosed. ACKNOWLEDGEMENTS I would like to thank my adviser, Professor Geoff Sutcliffe, for all the help and guidance he has given to me. He stimulated my interest in doing research and taught me how to think as a scientist. When I was stuck in my research, he was always patient and supportive. I feel so honored to have this excellent professor as my advisor. I would like to thank Professor Christian Duncan and Professor Miroslav Kubat for
DoubleNegation Elimination in Some Propositional Logics
"... This article answers two questions posed in the literature each concerning the guaranteed existence of proofs free of double negation A proof is free of double negation if none of its deduced steps contains a term of the form nnt for some term t where n denotes negation The rst question asks fo ..."
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This article answers two questions posed in the literature each concerning the guaranteed existence of proofs free of double negation A proof is free of double negation if none of its deduced steps contains a term of the form nnt for some term t where n denotes negation The rst question asks for conditions on the hypotheses that if satised guarantee the existence of a doublenegation free proof when the conclusion is free of double negation The second question asks about the existence of an axiom system for classical propositional calculus whose use for theorems with a conclusion free of double negation guarantees the existence of a doublenegationfree proof After giving conditions that answer the rst question we answer the second question by focusing on the Lukasiewicz threeaxiom system We then extend our studies to innitevalued sentential calculus and to intuitionistic logic and generalize the notion of being double negation free The doublenegation proofs of interest rely exclusively on the inference rule condensed detachment a rule that combines modus ponens with
Abstract
, 2008
"... This article answers two questions (posed in the literature), each concerning the guaranteed existence of proofs free of double negation. A proof is free of double negation if none of its deduced steps contains a term of the form n(n(t)) for some term t, where n denotes negation. The first question ..."
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This article answers two questions (posed in the literature), each concerning the guaranteed existence of proofs free of double negation. A proof is free of double negation if none of its deduced steps contains a term of the form n(n(t)) for some term t, where n denotes negation. The first question asks for conditions on the hypotheses that, if satisfied, guarantee the existence of a doublenegationfree proof when the conclusion is free of double negation. The second question asks about the existence of an axiom system for classical propositional calculus whose use, for theorems with a conclusion free of double negation, guarantees the existence of a doublenegationfree proof. After giving conditions that answer the first question, we answer the second question by focusing on the Lukasiewicz threeaxiom system. We then extend our studies to infinitevalued sentential calculus and to intuitionistic logic and generalize the notion of being doublenegation free. The doublenegation proofs of interest rely exclusively on the inference rule condensed detachment, a rule that combines modus ponens with an appropriately general rule of substitution. The automated reasoning program
A Spectrum of Applications of Automated Reasoning
, 2002
"... The likelihood of an automated reasoning program being of substantial assistance for a wide spectrum of applications rests with the nature of the options and parameters it o ers on which to base needed strategies and methodologies. This article focuses on such a spectrum, featuring W. McCune's ..."
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The likelihood of an automated reasoning program being of substantial assistance for a wide spectrum of applications rests with the nature of the options and parameters it o ers on which to base needed strategies and methodologies. This article focuses on such a spectrum, featuring W. McCune's program OTTER, discussing widely varied successes in answering open questions, and touching on some of the strategies and methodologies that played a key role. The applications include nding a rst proof, discovering single axioms, locating improved axiom systems, and simplifying existing proofs. The last application is directly pertinent to the recently found (by R. Thiele) Hilbert's twentyfourth problemwhich is extremely amenable to attack with the appropriate automated reasoning programa problem concerned with proof simpli cation. The methodologies include those for seeking shorter proofs and for nding proofs that avoid unwanted lemmas or classes of term, a speci c option for seeking proofs with smaller equational or formula complexity, and a di erent option to address the variable richness of a proof. The type of proof one obtains with the use of OTTER is Hilbertstyle
EN
, 2008
"... HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte p ..."
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HAL is a multidisciplinary open access archive for the deposit and dissemination of scientific research documents, whether they are published or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers. L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et a ̀ la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés. appor t de r ech er ch e