Skip to Main content Skip to Navigation
Conference papers

Vector Addition Systems Reachability Problem (A Simpler Solution)

Abstract : The reachability problem for Vector Addition Systems (VASs) is a central problem of net theory. The general problem is known to be decidable by algorithms based on the classical Kosaraju-Lambert-Mayr-Sacerdote-Tenney decomposition (KLMTS decomposition). Recently from this decomposition, we deduced that a final configuration is not reachable from an initial one if and only if there exists a Presburger inductive invariant that contains the initial configuration but not the final one. Since we can decide if a Preburger formula denotes an inductive invariant, we deduce from this result that there exist checkable certificates of non-reachability in the Presburger arithmetic. In particular, there exists a simple algorithm for deciding the general VAS reachability problem based on two semi-algorithms. A first one that tries to prove the reachability by enumerating finite sequences of actions and a second one that tries to prove the non-reachability by enumerating Presburger formulas. In another recent paper we provided the first proof of the VAS reachability problem that is not based on the KLMST decomposition. The proof is based on the notion of production relations that directly proves the existence of Presburger inductive invariants. In this paper we propose new intermediate results that dramatically simplify this last proof.
Complete list of metadatas

Cited literature [14 references]  Display  Hide  Download

https://hal.archives-ouvertes.fr/hal-00674970
Contributor : Jérôme Leroux <>
Submitted on : Sunday, May 20, 2012 - 1:01:34 PM
Last modification on : Thursday, January 11, 2018 - 6:20:17 AM
Document(s) archivé(s) le : Thursday, December 15, 2016 - 8:29:33 AM

File

main.pdf
Files produced by the author(s)

Identifiers

  • HAL Id : hal-00674970, version 3

Collections

Citation

Jérôme Leroux. Vector Addition Systems Reachability Problem (A Simpler Solution). The Alan Turing Centenary Conference, Jun 2012, Manchester, United Kingdom. pp.214-228. ⟨hal-00674970v3⟩

Share

Metrics

Record views

1264

Files downloads

712