Chapter

Computer Aided Verification

Volume 6174 of the series Lecture Notes in Computer Science pp 227-242

Fast Acceleration of Ultimately Periodic Relations

  • Marius BozgaAffiliated withVERIMAG, CNRS
  • , Radu IosifAffiliated withVERIMAG, CNRS
  • , Filip KonečnýAffiliated withVERIMAG, CNRSFIT BUT

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Abstract

Computing transitive closures of integer relations is the key to finding precise invariants of integer programs. In this paper, we describe an efficient algorithm for computing the transitive closures of difference bounds, octagonal and finite monoid affine relations. On the theoretical side, this framework provides a common solution to the acceleration problem, for all these three classes of relations. In practice, according to our experiments, the new method performs up to four orders of magnitude better than the previous ones, making it a promising approach for the verification of integer programs.