How Hard is It to Verify Flat Affine Counter Systems with the Finite Monoid Property?

  • Radu Iosif
  • Arnaud Sangnier
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9938)


We study several decision problems for counter systems with guards defined by convex polyhedra and updates defined by affine transformations. In general, the reachability problem is undecidable for such systems. Decidability can be achieved by imposing two restrictions: (1) the control structure of the counter system is flat, meaning that nested loops are forbidden, and (2) the multiplicative monoid generated by the affine update matrices present in the system is finite. We provide complexity bounds for several decision problems of such systems, by proving that reachability and model checking for Past Linear Temporal Logic stands in the second level of the polynomial hierarchy \(\varSigma ^P_2\), while model checking for First Order Logic is PSPACE-complete.


Model Check Transition Rule Counter System Affine Function Kripke Structure 
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© Springer International Publishing AG 2016

Authors and Affiliations

  1. 1.Verimag, Université Grenoble Alpes, CNRSGrenobleFrance
  2. 2.IRIF, Université Paris Diderot, CNRSParisFrance

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