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The Well Structured Problem for Presburger Counter Machines

Authors Alain Finkel, Ekanshdeep Gupta

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  • 15 pages

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Author Details

Alain Finkel
  • LSV, ENS Paris-Saclay, CNRS, Université Paris-Saclay, IUF, France
Ekanshdeep Gupta
  • Chennai Mathematical Institute, Chennai, India

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Alain Finkel and Ekanshdeep Gupta. The Well Structured Problem for Presburger Counter Machines. In 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 150, pp. 41:1-41:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2019)


We introduce the well structured problem as the question of whether a model (here a counter machine) is well structured (here for the usual ordering on integers). We show that it is undecidable for most of the (Presburger-defined) counter machines except for Affine VASS of dimension one. However, the strong well structured problem is decidable for all Presburger counter machines. While Affine VASS of dimension one are not, in general, well structured, we give an algorithm that computes the set of predecessors of a configuration; as a consequence this allows to decide the well structured problem for 1-Affine VASS.

Subject Classification

ACM Subject Classification
  • Theory of computation → Logic and verification
  • Theory of computation → Verification by model checking
  • Well structured transition systems
  • infinite state systems
  • Presburger counter machines
  • reachability
  • coverability


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