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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The author gratefully acknowledges financial support from the European Research Council, ERC grant agreement 339691, within the context of the project Feasibility, Logic and Randomness (FEALORA).
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de Oliveira Oliveira, M. (2016). Causality in Bounded Petri Nets is MSO Definable. In: Väänänen, J., Hirvonen, Å., de Queiroz, R. (eds) Logic, Language, Information, and Computation. WoLLIC 2016. Lecture Notes in Computer Science(), vol 9803. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-52921-8_13
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