Series-parallel posets: Algebra, automata and languages [chapter]

K. Lodaya, P. Weil
1998 Lecture Notes in Computer Science  
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 rst 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
more » ... notion of branching automaton. We show both a Myhill-Nerode theorem and a Kleene theorem. We also look at generalizations.
doi:10.1007/bfb0028590 fatcat:76pd54rcvvanldopkvpx54pcii