Series-Parallel Posets: Algebra, Automata and Languages

  title={Series-Parallel Posets: Algebra, Automata and Languages},
  author={Kamal Lodaya and Pascal Weil},
  • K. Lodaya, P. Weil
  • Published in STACS 25 February 1998
  • Mathematics, 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 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… 
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