Anti-unification algorithms and their applications in program analysis

  • Authors:

  • Peter E. Bulychev;Egor V. Kostylev;Vladimir A. Zakharov

  • Affiliations:

  • Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia;Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia;Faculty of Computational Mathematics and Cybernetics, Moscow State University, Moscow, Russia

  • Venue:
  • PSI'09 Proceedings of the 7th international Andrei Ershov Memorial conference on Perspectives of Systems Informatics
  • Year:
  • 2009

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Abstract

A term t is called a template of terms t1 and t2 iff t1=tη1 and t2=tη2, for some substitutions η1 and η2. A template t of t1 and t2 is called the most specific iff for any template t′ of t1 and t2 there exists a substitution ξ such that t=t′ξ. The anti-unification problem is that of computing the most specific template of two given terms. This problem is dual to the well-known unification problem, which is the computing of the most general instance of terms. Unification is used extensively in automatic theorem proving and logic programming. We believe that anti-unification algorithms may have wide applications in program analysis. In this paper we present an efficient algorithm for computing the most specific templates of terms represented by labelled directed acyclic graphs and estimate the complexity of the anti-unification problem. We also describe techniques for invariant generation and software clone detection based on the concepts of the most specific templates and anti-unification.