Logic and Rational Languages of Words Indexed by Linear Orderings

We prove that every rational language of words indexed by linear orderings is definable in monadic second-order logic. We also show that the converse is true for the class of languages indexed by countable scattered linear orderings, but false in the general case. As a corollary we prove that the inclusion problem for rational languages of words indexed by countable linear orderings is decidable.

• Type: Conference
• Year: 2008
• Where: CSR
• Authors: Nicolas Bedon, Alexis Bès, Olivier Carton, Chloe Rispal
• Keywords: CSR 2008, Linear Orderings, Monadic Second-order Logic, Rational Languages, Theoretical Computer Science