Languages and models for hybrid automata: A coalgebraic perspective

Neves, Renato; Barbosa, Lu­ís Soares

doi:10.1016/j.tcs.2017.09.038

Theoretical Computer Science

2018

DOI: 10.1016/j.tcs.2017.09.038

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Languages and models for hybrid automata: A coalgebraic perspective

Renato Neves

Luís Soares Barbosa

Abstract: We study hybrid automata from a coalgebraic point of view. We show that such a perspective supports a generic theory of hybrid automata with a rich palette of definitions and results. This includes, among other things, notions of bisimulation and behaviour, state minimisation techniques, and regular expression languages.

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“…Hybrid automata specifying both discrete and continuous behavior can also be modeled as coalgebras [24]. A coalgebraic perspective supporting a generic theory of hybrid automata with a rich palette of definitions and results is studied in [25]. In addition, a coalgebraic semantics framework for quantum systems is developed in [26].…”

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Fuzzy Automata as Coalgebras

Wang

Barbosa

et al. 2021

Mathematics

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The coalgebraic method is of great significance to research in process algebra, modal logic, object-oriented design and component-based software engineering. In recent years, fuzzy control has been widely used in many fields, such as handwriting recognition and the control of robots or air conditioners. It is then an interesting topic to analyze the behavior of fuzzy automata from a coalgebraic point of view. This paper models different types of fuzzy automata as coalgebras with a monad structure capturing fuzzy behavior. Based on the coalgebraic models, we can define a notion of fuzzy language and consider several versions of bisimulation for fuzzy automata. A group of combinators is defined to compose fuzzy automata of two branches: state transition and output function. A case study illustrates the coalgebraic models proposed and their composition.

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confidence: 99%

Fuzzy Automata as Coalgebras

Wang

Barbosa

et al. 2021

Mathematics

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Hybrid automaton-based disturbance-aware predictive control with receding horizon optimization for three-phase full-bridge inverters

Chen

Shen

2022

Control Engineering Practice

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Limits in categories of Vietoris coalgebras

Hofmann¹,

Neves²,

Nora³

2018

Math. Struct. Comp. Sci.

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Motivated by the need to reason about hybrid systems, we study limits in categories of coalgebras whose underlying functor is a Vietoris polynomial one -intuitively, the topological analogue of a Kripke polynomial functor. Among other results, we prove that every Vietoris polynomial functor admits a final coalgebra if it respects certain conditions concerning separation axioms and compactness.When the functor is restricted to some of the categories induced by these conditions the resulting categories of coalgebras are even complete.As a practical application, we use these developments in the specification and analysis of nondeterministic hybrid systems, in particular to obtain suitable notions of stability, and behaviour.

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Languages and models for hybrid automata: A coalgebraic perspective

Cited by 3 publications

References 21 publications

Fuzzy Automata as Coalgebras

Fuzzy Automata as Coalgebras

Hybrid automaton-based disturbance-aware predictive control with receding horizon optimization for three-phase full-bridge inverters

Limits in categories of Vietoris coalgebras

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