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A Coalgebraic Take on Regular and omega-Regular Behaviour for Systems with Internal Moves

Author Tomasz Brengos

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Tomasz Brengos
  • Faculty of Mathematics and Information Science, Warsaw University of Technology, ul. Koszykowa 75, 00-662 Warszawa, Poland

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Tomasz Brengos. A Coalgebraic Take on Regular and omega-Regular Behaviour for Systems with Internal Moves. In 29th International Conference on Concurrency Theory (CONCUR 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 118, pp. 25:1-25:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)
https://doi.org/10.4230/LIPIcs.CONCUR.2018.25

Abstract

We present a general coalgebraic setting in which we define finite and infinite behaviour with Büchi acceptance condition for systems with internal moves. Since systems with internal moves are defined here as coalgebras for a monad, in the first part of the paper we present a construction of a monad suitable for modelling (in)finite behaviour. The second part of the paper focuses on presenting the concepts of a (coalgebraic) automaton and its (omega-) behaviour. We end the paper with coalgebraic Kleene-type theorems for (omega-) regular input. We discuss the setting in the context of non-deterministic (tree) automata and Segala automata.

Subject Classification

ACM Subject Classification
  • Theory of computation → Models of computation
Keywords
  • coalgebras
  • regular languages
  • omega regular languages
  • automata
  • Büchi automata
  • silent moves
  • internal moves
  • monads
  • saturation

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