In order to model concurrency, we extend automata theory from the usual word languages (sets of labelled linear orders) to sets of labelled series-parallel posets - or, equivalently, to sets of terms in an algebra with two product operations: sequential and parallel. We first consider languages of posets having bounded width, and characterize them using depth-nilpotent algebras. Next we introduce series-rational expressions, a natural generalization of the usual rational expressions, as well as a notion of branching automaton. We show both a Myhill-Nerode theorem and a Kleene theorem. We also look at generalizations. © 1998 Springer-Verlag.
CITATION STYLE
Lodaya, K., & Weil, P. (1998). Series-parallel posets: Algebra, automata and languages. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1373 LNCS, pp. 555–565). https://doi.org/10.1007/BFb0028590
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