TL;DR
This paper explores the deep connections between 2D topological quantum field theories, formal language theory, and logic, establishing equivalences and special cases that bridge physics, computer science, and mathematics.
Contribution
It introduces a novel correspondence between 2D TQFTs and formal languages, and reformulates these relations using second order monadic logic.
Findings
Equivalence of 2D closed TFTs and rational exchangeable series
Relation between TQFTs and recognisable weighted formal languages
Special case analysis for finite groups
Abstract
We establish a relation between fully extended -dimensional TQFTs and recognisable weighted formal languages, rational biprefix codes and lattice TFTs. We show the equivalence of closed TFTs and rational exchangeable series and we discuss the important special case of finite groups. Finally, we outline a reformulation in terms of a restricted version of second order monadic logic.
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Taxonomy
Topicssemigroups and automata theory · Algebraic structures and combinatorial models · Coding theory and cryptography