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Communication Dans Un Congrès Année : 2009

The General Vector Addition System Reachability Problem by Presburger Inductive Invariants

Résumé

The reachability problem for Vector Addition Systems (VASs) is a central problem of net theory. The general problem is known decidable by algorithms exclusively based on the classical Kosaraju-Lambert-Mayr-Sacerdote-Tenney decomposition. This decomposition is used in this paper to prove that the Parikh images of languages accepted by VASs are \emph{semi-pseudo-linear}; a class that extends the semi-linear sets, a.k.a. the sets definable in the Presburger arithmetic. We provide an application of this result; we prove that a final configuration is not reachable from an initial one if and only if there exists a Presburger formula denoting a forward 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 that there exist checkable certificates of non-reachability. 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.

Domaines

Autre Autre [cs.OH]
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Dates et versions

hal-00272667 , version 1 (11-04-2008)
hal-00272667 , version 2 (11-04-2008)
hal-00272667 , version 3 (27-05-2008)
hal-00272667 , version 4 (28-05-2008)
hal-00272667 , version 5 (04-06-2008)
hal-00272667 , version 6 (11-07-2008)
hal-00272667 , version 7 (08-09-2008)
hal-00272667 , version 8 (29-10-2008)
hal-00272667 , version 9 (22-01-2009)
hal-00272667 , version 10 (28-04-2009)
hal-00272667 , version 11 (29-04-2009)
hal-00272667 , version 12 (08-06-2009)

Identifiants

  • HAL Id : hal-00272667 , version 12

Citer

Jérôme Leroux. The General Vector Addition System Reachability Problem by Presburger Inductive Invariants. Logic in Computer Science (LICS 2009), Aug 2009, Los Angeles, United States. pp.4-13. ⟨hal-00272667v12⟩

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