Abstract
We present an automata-theoretic framework for the model checking of true concurrency properties. These are specified in a fixpoint logic, corresponding to history-preserving bisimilarity, capable of describing events in computations and their dependencies. The models of the logic are event structures or any formalism which can be given a causal semantics, like Petri nets. Given a formula and an event structure satisfying suitable regularity conditions we show how to construct a parity tree automaton whose language is non-empty if and only if the event structure satisfies the formula. The automaton, due to the nature of event structure models, is usually infinite. We discuss how it can be quotiented to an equivalent finite automaton, where emptiness can be checked effectively. In order to show the applicability of the approach, we discuss how it instantiates to finite safe Petri nets. As a proof of concept we provide a model checking tool implementing the technique.
Highlights
In a recent paper [26] we proved the decidability of the problem for the alternation free fragment of the logic Lhp over a class of event structures satisfying a suitable regularity condition [27] referred to as strong regularity
We show how the model checking approach outlined before can be instantiated on finite safe Petri nets, a classical model of concurrency and distribution [32], by identifying a suitable effective bisimulation equivalence on the nondeterministic parity tree automaton (NPA)
We introduced an automata-theoretic framework for the model checking of the logic for true concurrency Lhp, representing the logical counterpart of a classical true concurrent equivalence, i.e., history preserving bisimilarity
Summary
Behavioural logics with the corresponding verification techniques are a cornerstone of automated verification. Event-based logics have been recently introduced [20,21], capable of uniformly characterising the equivalences in the true concurrent spectrum. While the relation between operational models, behavioural equivalences and event-based true concurrent logics is well understood, the corresponding model checking problem has received limited attention. In a recent paper [26] we proved the decidability of the problem for the alternation free fragment of the logic Lhp over a class of event structures satisfying a suitable regularity condition [27] referred to as strong regularity. Besides providing an alternative approach for model-checking Lhp, amenable of a more efficient implementation, this generalises the decidability result of [26] to the full logic Lhp. Given a formula in Lhp and a strongly regular event structure, the procedure generates a parity tree automaton.
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