Boolean TQFTs with accumulating defects, sofic systems, and automata for infinite words

Abstract

Any finite state automaton gives rise to a Boolean one-dimensional TQFT with defects and inner endpoints of cobordisms. This paper extends the correspondence to Boolean TQFTs where defects accumulate toward inner endpoints, relating such TQFTs and topological theories to sofic systems and $\omega$-automata.

31 pages, many figures