Strong Termination for Gap-Order Constraint Abstractions of Counter Systems

  • Laura Bozzelli
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7183)


We address termination analysis for the class of gap-order constraint systems (GCS), an (infinitely-branching) abstract model of counter machines recently introduced in [8], in which constraints (over ℤ) between the variables of the source state and the target state of a transition are gap-order constraints (GC) [18]. GCS extend monotonicity constraint systems [4], integral relation automata [9], and constraint automata in [12]. Since GCS are infinitely-branching, termination does not imply strong termination, i.e. the existence of an upper bound on the lengths of the runs from a given state. We show the following: (1) checking strong termination for GCS is decidable and Pspace-complete, and (2) for each control location of the given GCS, one can build a GC representation of the set of variable valuations from which strong termination does not hold.


Strong Termination Counter System Counter Machine Monotonicity Graph Variable Valuation 
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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Laura Bozzelli
    • 1
  1. 1.Technical University of Madrid (UPM)MadridSpain

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