The pseudofinite monadic second order theory of words
Logic
2022-03-14 v2 Logic in Computer Science
Abstract
We analyse the pseudofinite monadic second order theory of words over a fixed finite alphabet. In particular we present an axiomatisation of this theory, working in a one-sorted first order framework. The analysis hinges on the fact that concatenation of words interacts nicely with monadic second order logic. More precisely, give a signature under which for each natural number k, equivalence of (monadic second order versions of) words with respect to formulas of quantifier depth at most k is a congruence for concatenation. We use our analysis to present an alternative proof of a theorem connecting recognisable languages and finitely generated free profinite monoids via extended Stone duality, due to Gehrke, Grigorieff, and Pin.
Keywords
Cite
@article{arxiv.2202.07774,
title = {The pseudofinite monadic second order theory of words},
author = {Deacon Linkhorn},
journal= {arXiv preprint arXiv:2202.07774},
year = {2022}
}