Series-parallel languages on scattered and countable posets

Abstract : 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 View the MathML source-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.
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https://hal.archives-ouvertes.fr/hal-00790113
Contributor : Chloé Rispal <>
Submitted on : Tuesday, February 19, 2013 - 2:25:13 PM
Last modification on : Friday, April 12, 2019 - 10:18:09 AM

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  • HAL Id : hal-00790113, version 1

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Nicolas Bedon, Chloé Rispal. Series-parallel languages on scattered and countable posets. Theoretical Computer Science, Elsevier, 2011, 412 (22), pp.2356-2369. ⟨hal-00790113⟩

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