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Equivalence between model-checking flat counter systems and Presburger arithmetic. (English) Zbl 1393.68100
Summary: We show that model-checking flat counter systems with the branching-time temporal logic CTL* extended with arithmetical constraints on counter values has the same worst-case complexity as the satisfiability problem for Presburger arithmetic. The lower bound already holds with strong restrictions: the logical language uses only the temporal operator EF and no arithmetical constraints, and the guards on the transitions are made of linear constraints. This work complements our understanding of model-checking flat counter systems with linear-time temporal logics, such as LTL, for which the problem is already known to be (only) NP-complete with guards restricted to the linear fragment.
MSC:
68Q60 Specification and verification (program logics, model checking, etc.)
03B44 Temporal logic
03F30 First-order arithmetic and fragments
68Q17 Computational difficulty of problems (lower bounds, completeness, difficulty of approximation, etc.)
Software:
TaPAS; z3; CVC4
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