## Tomasz Brengos - A coalgebraic take on regular and $\omega$-regular behaviours

lmcs:5179 - Logical Methods in Computer Science, December 23, 2021, Volume 17, Issue 4 - https://doi.org/10.46298/lmcs-17(4:24)2021
A coalgebraic take on regular and $\omega$-regular behaviours

Authors: Tomasz Brengos

We present a general coalgebraic setting in which we define finite and infinite behaviour with Büchi acceptance condition for systems whose type is a monad. The first part of the paper is devoted to presenting 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. The framework is instantiated on non-deterministic (Büchi) automata, tree automata and probabilistic automata.

Volume: Volume 17, Issue 4
Published on: December 23, 2021
Accepted on: October 27, 2021
Submitted on: February 8, 2019
Keywords: Computer Science - Logic in Computer Science