Reachability in Two-Dimensional Vector Addition Systems with States Is PSPACE-Complete

Known to be decidable since 1981, there still remains a huge gap between the best known lower and upper bounds for the reach ability problem for vector addition systems with states (VASS). Here the problem is shown PSPACE-complete in the two-dimensional case, vastly improving on the doubly exponenti...

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Bibliographic Details
Published in2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 32 - 43
Main Authors Blondin, Michael, Finkel, Alain, Goller, Stefan, Haase, Christoph, McKenzie, Pierre
Format Conference Proceeding
LanguageEnglish
Published IEEE 01.07.2015
Subjects
Automata
bounded regular languages
Complexity theory
Encoding
Parikh images
Petri nets
Polynomials
Radiation detectors
reachability
semi-linear sets
Upper bound
vector addition systems with states
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Summary:Known to be decidable since 1981, there still remains a huge gap between the best known lower and upper bounds for the reach ability problem for vector addition systems with states (VASS). Here the problem is shown PSPACE-complete in the two-dimensional case, vastly improving on the doubly exponential time bound established in 1986 by Howell, Rosier, Huynh and Yen. Cover ability and bounded ness for two-dimensional VASS are also shown PSPACE-complete, and reach ability in two-dimensional VASS and in integer VASS under unary encoding are considered.
ISSN:1043-6871
2575-5528
DOI:10.1109/LICS.2015.14