Logic and Bounded-Width Rational Languages of Posets over Countable Scattered Linear Orderings

Authors:
Nicolas Bedon
Affiliations:
Laboratoire d'informatique de l'Institut Gaspard Monge, UMR CNRS 8049, Université Paris-Est and CNRS, Marne-la-Vallée Cedex 2, France 77454
Venue:
LFCS '09 Proceedings of the 2009 International Symposium on Logical Foundations of Computer Science
Year:
2009

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Abstract

In this paper we consider languages of labelled N-free posets over countable and scattered linear orderings. We prove that a language of such posets is series-rational if and only if it is recognizable by a finite depth-nilpotent algebra if and only if it is bounded-width and monadic second-order definable. This extends previous results on languages of labelled N-free finite and ω-posets and on languages of labelled countable and scattered linear orderings.