Solving Coverability Problem for Monotonic Counter Systems by Supercompilation

  • Andrei V. Klimov
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7162)

Abstract

We put the program transformation method known as supercompilation in the context of works on counter systems, well-structured transition systems, Petri nets, etc. Two classic versions of the supercompilation algorithm are formulated for counter systems, using notions and notation adopted from the literature on transition systems.

A procedure to solve the coverability problem for a counter system by iterative application of a supercompiler to the system along with initial and target sets of states, is presented. Its correctness for monotonic counter systems provided the target set is upward-closed and the initial set has a certain form, is proved.

The fact that a supercompiler can solve the coverability problem for a lot of practically interesting counter systems has been discovered by A. Nemytykh and A. Lisitsa when they performed experiments on verification of cache-coherence protocols and other models by means of the Refal supercompiler SCP4, and since then theoretical explanation why this was so successful has been an open problem. Here the solution for the monotonic counter systems is given.

Keywords

supercompilation verification reachability coverability well-structured transition systems counter systems 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Andrei V. Klimov
    • 1
  1. 1.Keldysh Institute of Applied MathematicsRussian Academy of SciencesMoscowRussia

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