An Online Proof-Producing Decision Procedure for Mixed-Integer Linear Arithmetic

  • Sergey Berezin
  • Vijay Ganesh
  • David L. Dill
Conference paper

DOI: 10.1007/3-540-36577-X_38

Part of the Lecture Notes in Computer Science book series (LNCS, volume 2619)
Cite this paper as:
Berezin S., Ganesh V., Dill D.L. (2003) An Online Proof-Producing Decision Procedure for Mixed-Integer Linear Arithmetic. In: Garavel H., Hatcliff J. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2003. Lecture Notes in Computer Science, vol 2619. Springer, Berlin, Heidelberg

Abstract

Efficient decision procedures for arithmetic play a very important role in formal verification. In practical examples, however, arithmetic constraints are often mixed with constraints from other theories like the theory of arrays, Boolean satisfiability (SAT), bit-vectors, etc. Therefore, decision procedures for arithmetic are especially useful in combination with other decision procedures. The framework for such a combination is implemented at Stanford in the tool called Cooperating Validity Checker (CVC) [SBD02].

This work augments CVC with a decision procedure for the theory of mixed integer linear arithmetic based on the Omega-test [Pug91] extended to be online and proof producing. These extensions are the most important and challenging part of the work, and are necessary to make the combination efficient in practice.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • Sergey Berezin
    • 1
  • Vijay Ganesh
    • 1
  • David L. Dill
    • 1
  1. 1.Stanford UniversityUSA

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