MPI-INF/SWS Research Reports 1991-2021

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Symbolic representation of upward-closed sets

Delzanno, Giorgio and Raskin, Jean-Francois

November 1999, 24 pages.

Status: available - back from printing

Computing the set of states backwards reachable from a given {\em upward-closed} set of initial states is decidable for infinite-state systems like `unbounded' Petri Nets, Vector Addition Systems, Lossy Petri Nets, and Broadcast Protocols. An abstract algorithm that solves the problem is given by When applied to this class of verification problems, traditional symbolic model checking methods suffer from the state explosion problem even for very small examples. We provide BDD-like data structure to represent in a compact way collections of upwards closed sets over numerical domains. This way, we turn the abstract algorithm of [ACJT96,FS99] into a practical method. Preliminary experimental results indicate the potential usefulness of our method.

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  AUTHOR = {Delzanno, Giorgio and Raskin, Jean-Francois},
  TITLE = {Symbolic representation of upward-closed sets},
  TYPE = {Research Report},
  INSTITUTION = {Max-Planck-Institut f{\"u}r Informatik},
  ADDRESS = {Stuhlsatzenhausweg 85, 66123 Saarbr{\"u}cken, Germany},
  NUMBER = {MPI-I-1999-2-007},
  MONTH = {November},
  YEAR = {1999},
  ISSN = {0946-011X},