Ordered Counter-Abstraction

Refinable Subword Relations for Parameterized Verification
  • Pierre Ganty
  • Ahmed Rezine
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8370)


We present an original refinable subword based symbolic representation for the verification of linearly ordered parameterized systems. Such a system consists of arbitrary many finite processes placed in an array. Processes communicate using global transitions constrained by their relative positions (i.e., priorities). The model can include binary communication, broadcast, shared variables or dynamic creation and deletion of processes. Configurations are finite words of arbitrary lengths. The successful monotonic abstraction approach uses the subword relation to define upward closed sets as symbolic representations for such systems. Natural and automatic refinements remained missing for such symbolic representations. For instance, subword based relations are simply too coarse for automatic forward verification of systems involving priorities. We remedy to this situation and introduce a symbolic representation based on an original combination of counter abstraction with subword based relations. This allows us to define an infinite family of relaxation operators that guarantee termination by a new well quasi ordering argument. The proposed automatic analysis is at least as precise and efficient as monotonic abstraction when performed backwards. It can also be successfully used in forward, something monotonic abstraction is incapable of. We implemented a prototype to illustrate the approach.


counter abstraction well quasi ordering reachability parameterized verification 


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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Pierre Ganty
    • 1
  • Ahmed Rezine
    • 2
  1. 1.IMDEA Software InstituteSpain
  2. 2.Linköping UniversitySweden

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