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A Finite Axiomatisation of Finite-State Automata Using String Diagrams

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arxiv 2211.16484 v3 pith:ZJO5DO2K submitted 2022-11-29 cs.LO cs.FL

Robin Piedeleu , Fabio Zanasi This is my paper · ORCID
classification cs.LOcs.FL
keywords automataaxiomatisationdiagramsfinitefinite-statestringablealgebraic
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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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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Foundations of Digital Circuits: Denotation, Operational, and Algebraic Semantics

    cs.LO 2025-02 conditional novelty 6.0 of 10

    A sound and complete denotational, operational, and algebraic semantics for synchronous sequential circuits with arbitrary feedback, plus a hypergraph rewriting framework for digital circuits.

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