Abstract. Determining the complexity of the reachability problem for vector addition systems with states (VASS) is a long-standing open problem in computer science. Long known to be decidable, the problem to this day lacks any complexity upper bound whatsoever. In this paper, reachability for two-dimensional VASS is shown PSPACE-complete. This improves on a previously known doubly exponential time bound established by Howell, Rosier, Huynh and Yen in 1986. The coverability and boundedness problems are also noted to be PSPACE-complete. In addition, some complexity results are given for the reachability problem in two-dimensional VASS and in integer VASS when numbers are encoded in unary.
Abstract. We investigate the decidability and complexity of various model checking problems over one-counter automata. More specifically, we consider succinct one-counter automata, in which additive updates are encoded in binary, as well as parametric one-counter automata, in which additive updates may be given as unspecified parameters. We fully determine the complexity of model checking these automata against CTL, LTL, and modal µ-calculus specifications.
Abstract-One-counter processes are pushdown systems over a singleton stack alphabet (plus a stack-bottom symbol). We study the complexity of two closely related verification problems over one-counter processes: model checking with the temporal logic EF, where formulas are given as directed acyclic graphs, and weak bisimilarity checking against finite systems. We show that both problems are P NP -complete. This is achieved by establishing a close correspondence with the membership problem for a natural fragment of Presburger Arithmetic, which we show to be P NP -complete. This fragment is also a suitable representation for the global versions of the problems. We also show that there already exists a fixed EF formula (resp. a fixed finite system) such that model checking (resp. weak bisimulation) over one-counter processes is hard for P NP [log] . However, the complexity drops to P if the onecounter process is fixed.
Abstract. This paper introduces a class of register machines whose registers can be updated by polynomial functions when a transition is taken, and the domain of the registers can be constrained by linear constraints. This model strictly generalises a variety of known formalisms such as various classes of Vector Addition Systems with States. Our main result is that reachability in our class is PSPACE-complete when restricted to one register. We moreover give a classification of the complexity of reachability according to the type of polynomials allowed and the geometry induced by the range-constraining formula.
Abstract-Given two pushdown automata, the bisimilarity problem asks whether the infinite transition systems they induce are bisimilar. While this problem is known to be decidable our main result states that it is nonelementary, improving EXPTIMEhardness, which was the best previously known lower bound for this problem. Our lower bound result holds for normed pushdown automata as well.
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