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arXiv · 2211.16484

A Finite Axiomatisation of Finite-State Automata Using String Diagrams

Robin Piedeleu·Fabio Zanasi
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Abstract

We develop a fully diagrammatic approach to finite-state automata, based on reinterpreting their usual state-transition graphical representation as a two-dimensional syntax of string diagrams. In this setting, we are able to provide a complete equational theory for language equivalence, with two notable features. First, the proposed axiomatisation is finite. Second, the Kleene star is a derived concept, as it can be decomposed into more primitive algebraic blocks.

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Robin Piedeleu, Fabio Zanasi. 2022-11-29. A Finite Axiomatisation of Finite-State Automata Using String Diagrams. https://doi.org/10.46298/lmcs-19(1%3A13)2023

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