Strong Termination for Gap-Order Constraint Abstractions of Counter Systems
We address termination analysis for the class of gap-order constraint systems (GCS), an (infinitely-branching) abstract model of counter machines recently introduced in , in which constraints (over ℤ) between the variables of the source state and the target state of a transition are gap-order constraints (GC) . GCS extend monotonicity constraint systems , integral relation automata , and constraint automata in . 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.
KeywordsStrong Termination Counter System Counter Machine Monotonicity Graph Variable Valuation
Unable to display preview. Download preview PDF.
- 1.Abdulla, P.A., Delzanno, G.: On the coverability problem for constrained multiset rewriting. In: Proc. 5th AVIS (2006)Google Scholar
- 4.Ben-Amram, A.: Size-change termination, monotonicity constraints and ranking functions. Logical Methods in Computer Science 6(3) (2010)Google Scholar
- 5.Ben-Amram, A., Vainer, M.: Complexity Analysis of Size-Change Terminating Programs. In: Second Workshop on Developments in Implicit Computational Complexity (2011)Google Scholar
- 7.Bozzelli, L.: Strong termination for gap-order constraint abstractions of counter systems. Technical report (2011), http://clip.dia.fi.upm.es/~lbozzelli
- 8.Bozzelli, L., Pinchinat, S.: Verification of gap-order constraint abstractions of counter systems. In: Proc. 13th VMCAI, Springer, Heidelberg (2012)Google Scholar
- 15.Jonson, N.D.: Computability and Complexity from a Programming Perspective. Foundations of Computing Series. MIT Press (1997)Google Scholar
- 16.Peterson, J.L.: Petri Net Theory and the Modelling of Systems. Prentice-Hall (1981)Google Scholar