A coalgebraic take on regular and $\omega$-regular behaviours

Brengos, Tomasz

doi:10.46298/lmcs-17(4:24)2021

Cited by 2 publications

(2 citation statements)

References 33 publications

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“…those found in alternating games. Another line is to extend the framework with results from the rich theory of coalgebras such as ω-behaviours [8], minimization [3], determinisation [43], and up-to techniques [4].…”

Section: Discussionmentioning

confidence: 99%

Behavioural equivalences for timed systems

Brengos¹,

Peressotti²

2019

Logical Methods in Computer Science ; Volume 15

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Timed transition systems are behavioural models that include an explicit treatment of time flow and are used to formalise the semantics of several foundational process calculi and automata. Despite their relevance, a general mathematical characterisation of timed transition systems and their behavioural theory is still missing. We introduce the first uniform framework for timed behavioural models that encompasses known behavioural equivalences such as timed bisimulations, timed language equivalences as well as their weak and time-abstract counterparts. All these notions of equivalences are naturally organised by their discriminating power in a spectrum. We prove that this result does not depend on the type of the systems under scrutiny: it holds for any generalisation of timed transition system. We instantiate our framework to timed transition systems and their quantitative extensions such as timed probabilistic systems.

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Section: Discussionmentioning

confidence: 99%

Behavioural equivalences for timed systems

Brengos¹,

Peressotti²

2019

Logical Methods in Computer Science ; Volume 15

Self Cite

View full text Add to dashboard Cite

show abstract

“…This paper is an extended version of [10] with all missing proofs and additional Section 6 where probabilistic (Büchi) automata are put into the framework.…”

Section: Introductionmentioning

confidence: 99%

A coalgebraic take on regular and $ω$-regular behaviours

Brengos

2019

Preprint

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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 (ω-) behaviour. We end the paper with coalgebraic Kleene-type theorems for (ω-) regular input. The framework is instantiated on non-deterministic (Büchi) automata, tree (Büchi) automata and probabilistic (Büchi) automata.

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A coalgebraic take on regular and $\omega$-regular behaviours

Cited by 2 publications

References 33 publications

Behavioural equivalences for timed systems

Behavioural equivalences for timed systems

A coalgebraic take on regular and $ω$-regular behaviours

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