An algebraic approach to MSO-definability on countable linear orderings

Autor:	Carton, Olivier, Colcombet, Thomas, Puppis, Gabriele
Rok vydání:	2017
Předmět:	Computer Science - Logic in Computer Science Computer Science - Formal Languages and Automata Theory
Druh dokumentu:	Working Paper
Popis:	We develop an algebraic notion of recognizability for languages of words indexed by countable linear orderings. We prove that this notion is effectively equivalent to definability in monadic second-order (MSO) logic. We also provide three logical applications. First, we establish the first known collapse result for the quantifier alternation of MSO logic over countable linear orderings. Second, we solve an open problem posed by Gurevich and Rabinovich, concerning the MSO-definability of sets of rational numbers using the reals in the background. Third, we establish the MSO-definability of the set of yields induced by an MSO-definable set of trees, confirming a conjecture posed by Bruy{\`e}re, Carton, and S{\'e}nizergues. Comment: The Journal of Symbolic Logic, Association for Symbolic Logic, In press
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/1702.05342 Zobrazit plný text záznamu View this record from Arxiv