The Well Structured Problem for Presburger Counter Machines

Abstract : 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.
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https://hal.archives-ouvertes.fr/hal-02305639
Contributor : Ekanshdeep Gupta <>
Submitted on : Friday, October 4, 2019 - 1:35:35 PM
Last modification on : Thursday, October 10, 2019 - 1:17:54 AM

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  • HAL Id : hal-02305639, version 1
  • ARXIV : 1910.02736

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Alain Finkel, Ekanshdeep Gupta. The Well Structured Problem for Presburger Counter Machines. 39th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2019), Arkadev Chattopadhyay; Paul Gastin, Dec 2019, Mumbai, India. ⟨hal-02305639⟩

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