Automatic decidability and combinability

  • Authors:

  • Christopher Lynch;Silvio Ranise;Christophe Ringeissen;Duc-Khanh Tran

  • Affiliations:

  • Department of Mathematics and Computer Science, P.O. Box 5815 Clarkson University, Potsdam, NY 13699-5815, USA;FBK-Irst, Via Sommarive 18, I-38100 Povo, Trento, Italy;LORIA - INRIA Lorraine, 615, rue du Jardin Botanique, BP 101, 54602 Villers-les-Nancy Cedex, France;School of Information and Communication Technology, Hanoi University of Science and Technology, 1 Dai Co Viet, Hanoi, Viet Nam

  • Venue:
  • Information and Computation
  • Year:
  • 2011

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Abstract

Verification problems can often be encoded as first-order validity or satisfiability problems. The availability of efficient automated theorem provers is a crucial pre-requisite for automating various verification tasks as well as their cooperation with specialized decision procedures for selected theories, such as Presburger Arithmetic. In this paper, we investigate how automated provers based on a form of equational reasoning, called paramodulation, can be used in verification tools. More precisely, given a theory T axiomatizing some data structure, we devise a procedure to answer the following questions. Is the satisfiability problem of T decidable by paramodulation? Can a procedure based on paramodulation for T be efficiently combined with other specialized procedures by using the Nelson-Oppen schema? Finally, if paramodulation decides the satisfiability problem of two theories, does it decide satisfiability in their union? The procedure capable of answering all questions above is based on Schematic Saturation; an inference system capable of over-approximating the inferences of paramodulation when solving satisfiability problems in a given theory T. Clause schemas derived by Schematic Saturation describe all clauses derived by paramodulation so that the answers to the questions above are obtained by checking that only finitely many different clause schemas are derived or that certain clause schemas are not derived.