Some connections between universal algebra and logics for trees
Mikołaj Bojańczyk, Henryk Michalewski · arXiv (Cornell University) · 2017
One of the major open problems in automata and logic is the following: is there an algorithm which inputs a regular tree language and decides if the language can be defined in first-order logic? The goal of this paper is to present this problem and similar ones using the language of universal algebra, highlighting potential connections to the structural theory of finite algebras, including Tame Congruence Theory.