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A Complete Diagrammatic Calculus for Automata Simulation

Authors Thibaut Antoine , Robin Piedeleu , Alexandra Silva , Fabio Zanasi

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LIPIcs.CSL.2025.27.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation
Keywords
  • finite-state automata
  • simulation
  • string diagrams
  • axiomatisation

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Abstract

We give a sound and complete (in)equational theory for simulation of finite state automata. Our approach uses a string diagrammatic calculus to represent automata and a functorial semantics to capture simulation in a compositional way. Interestingly, in contrast to other approaches based on regular expressions, fixpoints are a derived notion in our calculus and the resulting axiomatisation is finitary.

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Thibaut Antoine, Robin Piedeleu, Alexandra Silva, and Fabio Zanasi. A Complete Diagrammatic Calculus for Automata Simulation. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 27:1-27:22, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.CSL.2025.27

Author Details

Thibaut Antoine
  • ENS Rennes, France
Robin Piedeleu
  • University College London, UK
Alexandra Silva
  • Cornell University, Ithaca, NY, USA
Fabio Zanasi
  • University College London, UK

Funding

Fabio Zanasi acknowledges support from epsrc EP/V002376/1, miur P2022HXNSC (prin 2022 pnrr - Next Generation EU), and aria Safeguarded AI TA1.1 grant n.8777242. The other authors acknowledge support from ERC grant Autoprobe (no. 101002697), ARIA Safeguarded AI program, and epsrc Standard Grant CLeVer (EP/S028641/1).

Acknowledgements

Fabio Zanasi conducted part of this research while affiliated with the University of Bologna, Italy.

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