Causality in Bounded Petri Nets is MSO Definable
Pages 200 - 214
Abstract
In this work we show that the causal behaviour of any bounded Petri net is definable in monadic second order MSO logic. Our proof relies in a definability vs recognizability result for DAGs whose edges and vertices can be covered by a constant number of paths. Our notion of recognizability is defined in terms of saturated slice automata, a formalism for the specification of infinite families of graphs. We show that a family $$\mathfrak {G}$$ of k-coverable DAGs is recognizable by a saturated slice automaton if and only if $$\mathfrak {G}$$ is definable in monadic second order logic. This result generalizes Büchi's theorem from the context of strings, to the context of k-coverable DAGs.
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Published: 16 August 2016
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