Liveness Verification of Reversal-Bounded Multicounter Machines with a Free Counter

The Complexity of Reversal-Bounded Model-Checking

“…In both cases Presburger formulae are built: our proof is based on a run analysis whereas the proof in [16, Theorem 1] builds directly the formula. We believe our treatment is more uniform and it generalizes notions presented in [19,10]. Moreover, our run analysis for proving Theorem 2 is interesting for its own sake, see [4].…”

“…However this does not entail that problems involving infinite runs are decidable, since infinite runs are not necessarily effectively representable in Presburger arithmetic, see e.g. [10]. In this paper, we study problems of the form: given a counter system S, a bound r ≥ 0 and a formula φ, is there an infinite r-reversal-bounded run ρ such that ρ |= φ.…”

“…Moreover, in the paper we deal with modelchecking involving linear-time temporal logics with past-time and future temporal operators and with arithmetical constraints on counter values. In [10], it is shown that ∃-Presburger-infinitely often problem for reversal-bounded counter automata (with guards made of Boolean combinations of the form x i ∼ k) is decidable. Moreover, ∃-Presburger-always problem for reversal-bounded counter automata is undecidable [10].…”

“…In [10], it is shown that ∃-Presburger-infinitely often problem for reversal-bounded counter automata (with guards made of Boolean combinations of the form x i ∼ k) is decidable. Moreover, ∃-Presburger-always problem for reversal-bounded counter automata is undecidable [10]. Our decidability results on model-checking refine these results in order to obtain new decidability results, by allowing a full LTL specification language with arithmetical constraints and by proposing new concepts for reversal-boundedness.…”

On Selective Unboundedness of VASS

“…A major property of such operational models is that reachability sets are effectively definable in Presburger arithmetic [28], which provides decision procedures for LTL existential model-checking and other related problems, see e.g. [12]. However, the class of reversal-bounded counter automata is not recursive [28] but a significant breakthrough is achieved in [20] by designing a procedure to determine when a VASS is reversalbounded (or weakly reversal-bounded as defined later), even though the decision procedure can be nonprimitive recursive in the worst-case.…”