Equivalence Between Model-Checking Flat Counter Systems and Presburger Arithmetic
Résumé
We show that model-checking flat counter systems over CTL* (with arithmetical constraints on counter values) has the same complexity as the satisfiability problem for Presburger arithmetic. The lower bound already holds with the temporal operator EF only, no~arithmetical constraints in the logical language and with guards on transitions made of simple linear constraints. This 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.
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