Abstract
In contrast to the classical setting of sequences, no temporal logic has yet been identified over Mazurkiewicz traces that is equivalent to first-order logic over traces and yet admits an elementary decision procedure. In this paper, we describe a local temporal logic over traces that is expressively complete and whose satisfiability problem is in Pspace. Contrary to the situation for sequences, past modalities are essential for such a logic. A somewhat unexpected corollary is that first-order logic with three variables is expressively complete for traces.
Work done while the second author was visiting LIAFA, Université Paris 7. Partial support of CEFIPRA-IFCPAR Project 2102-1 (ACSMV) is gratefully acknowledged.
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Gastin, P., Mukund, M. (2002). An Elementary Expressively Complete Temporal Logic for Mazurkiewicz Traces. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_80
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