Pomsets for local trace languages

Authors:
Dietrich Kuske;Rémi Morin
Affiliations:
Institut für Algebra, Technische Universität Dresden, D-01062 Dresden, Germany;LIF - Laboratoire d'Informatique Fondamentale, Université de Provence, 39, rue F. Joliot Curie, F-13453 Marseille Cedex 13, France
Venue:
Journal of Automata, Languages and Combinatorics - Selected papers of the workshop on logic and algebra for concurrency
Year:
2001

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Abstract

Mazurkiewicz traces can be seen as equivalence classes of words or as pomsets. Their generalization by local traces was formalized by HOOGERS, KLEIJN and THIAGARAJAN as equivalence classes of step firing sequences. First we introduce a pomset representation for local traces. Extending Büchi's Theorem and a previous generalization to Mazurkiewicz traces, we show then that a local trace language is recognized by a finite step transition system if and only if its class of pomsets is bounded and definable in Monadic Second Order logic.