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

Mee Seong Im; Mikhail Khovanov; Paul Gustafson

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

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arxiv 2312.17033 v1 pith:ERJVZYWT submitted 2023-12-25 math.CT cs.FLmath-phmath.DSmath.MPmath.QA

Paul Gustafson , Mee Seong Im , Mikhail Khovanov This is my paper · ORCID

classification math.CTcs.FLmath-phmath.DSmath.MPmath.QA

keywords booleandefectstqftsautomataendpointsinnersoficsystems

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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.

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Formal Languages and TQFTs with Defects
math-ph 2024-12 conditional novelty 6.0 of 10

A Boolean 1D TQFT-with-defects construction for regular languages is shown to be functorial under transducers and generalized to context-free grammars via an operadic Chomsky-Schützenberger theorem.

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