Reachability for Bounded Branching VASS

In this paper we consider the reachability problem for bounded branching VASS. Bounded VASS are a variant of the classic VASS model where all values in all configurations are upper bounded by a fixed natural number, encoded in binary in the input. This model gained a lot of attention in 2012 when Haase et al. showed its connections with timed automata. Later in 2013 Fearnley and Jurdzi\'{n}ski proved that the reachability problem in this model is PSPACE-complete even in dimension 1. Here, we investigate the complexity of the reachability problem when the model is extended with branching transitions, and we prove that the problem is EXPTIME-complete when the dimension is 2 or larger.

[1]  G. Grammin.  Polynomial-time Algorithm , 1984 .

[2]  Mihalis Yannakakis,et al.  Minimum and maximum delay problems in real-time systems , 1991, Formal Methods Syst. Des..

[3]  Patrick Totzke,et al.  Reachability in Two-Dimensional Unary Vector Addition Systems with States is NL-Complete* , 2016, 2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).

[4]  Mikolaj Bojanczyk.  Automata column , 2014, SIGL.

[5]  Ernst W. Mayr.  An Algorithm for the General Petri Net Reachability Problem , 1984, SIAM J. Comput..

[6]  Alain Finkel,et al.  Reachability in Register Machines with Polynomial Updates , 2013, MFCS.

[7]  Rajeev Alur,et al.  A Theory of Timed Automata , 1994, Theor. Comput. Sci..

[8]  Grégoire Sutre,et al.  Polynomial-Space Completeness of Reachability for Succinct Branching VASS in Dimension One , 2017, ICALP.

[9]  Joël Ouaknine,et al.  On the Relationship between Reachability Problems in Timed and Counter Automata , 2012, RP.

[10]  Alain Finkel,et al.  Reachability in Two-Dimensional Vector Addition Systems with States Is PSPACE-Complete , 2014, 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science.

[11]  Ahmed Bouajjani,et al.  Analysis of recursively parallel programs , 2012, POPL '12.

[12]  Slawomir Lasota,et al.  Regular separability of one counter automata , 2017, 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).

[13]  Joël Ouaknine,et al.  Reachability in Succinct and Parametric One-Counter Automata , 2009, CONCUR.

[14]  Lorenzo Clemente,et al.  Timed pushdown automata and branching vector addition systems , 2017, 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).

[15]  John Fearnley,et al.  Reachability in two-clock timed automata is PSPACE-complete , 2015, Inf. Comput..

[16]  Christoph Haase,et al.  A Polynomial-Time Algorithm for Reachability in Branching VASS in Dimension One , 2016, ICALP.

[17]  Rich Schroeppel,et al.  A Two Counter Machine Cannot Calculate 2N , 1972 .

[18]  Leslie G. Valiant,et al.  Deterministic One-Counter Automata , 1975, J. Comput. Syst. Sci..

[19]  Sylvain Schmitz,et al.  Reachability in Vector Addition Systems is Primitive-Recursive in Fixed Dimension , 2019, 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS).