Chloé Rispal

TL;DR: It is proved that every rational language of words indexed by linear orderings is definable in monadic second-order logic, and it is shown that the converse is true for the class of languages indexed by countable scattered linear ordering, but false in the general case.

TL;DR: It is established 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.

TL;DR: The class of labelled posets considered in this paper is the smallest containing letters, closed under finite parallel operation and sequential product indexed by all countable and scattered linear orderings, which establishes that those labelledPosets are precisely the N-free ones.