Series-parallel languages and the bounded-width property
Theoretical Computer Science
Rationality in algebras with a series operation
Information and Computation
Infinite Series-Parallel Posets: Logic and Languages
ICALP '00 Proceedings of the 27th International Colloquium on Automata, Languages and Programming
Series-Parallel Posets: Algebra, Automata and Languages
STACS '98 Proceedings of the 15th Annual Symposium on Theoretical Aspects of Computer Science
Towards a language theory for infinite N-free pomsets
Theoretical Computer Science
Logic and Bounded-Width Rational Languages of Posets over Countable Scattered Linear Orderings
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
DLT'02 Proceedings of the 6th international conference on Developments in language theory
Series-parallel languages on scattered and countable posets
MFCS'07 Proceedings of the 32nd international conference on Mathematical Foundations of Computer Science
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In this paper, we investigate the recognition by finite automata of languages of countable labelled posets. We unify and generalize several previous results from two different directions: the theory of finite or @wN-free posets, and automata over countable and scattered linear orderings. First, we establish that the smallest class of posets obtained from the empty set and the singleton and closed under finite parallel operation and sequential concatenation indexed by all linear orderings corresponds precisely to the class of scattered and countable N-free posets without infinite antichains. Next, we prove a Kleene-like theorem. We define automata and rational expressions for languages of countable, scattered, N-free labelled posets without infinite antichains, and show that both formalisms have the same expressive power.