On Coalgebras with Internal Moves

Brengos, Tomasz

doi:10.1007/978-3-662-44124-4_5

Cited by 7 publications

(19 citation statements)

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“…A promising direction is to follow this connection between modal logic and SOS, taking advantage of the bialgebraic presentation of ULTraS provided in this paper. Another direction is to investigate the implications of recent developments in the coalgebraic understanding of internal moves for systems generalized by ULTraSs such as Weighted LTS [20] and Segala systems [6].…”

Section: Discussionmentioning

confidence: 99%

GSOS for non-deterministic processes with quantitative aspects

Miculan

Peressotti

2014

Electron. Proc. Theor. Comput. Sci.

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Recently, some general frameworks have been proposed as unifying theories for processes combining non-determinism with quantitative aspects (such as probabilistic or stochastically timed executions), aiming to provide general results and tools. This paper provides two contributions in this respect. First, we present a general GSOS specification format (and a corresponding notion of bisimulation) for non-deterministic processes with quantitative aspects. These specifications define labelled transition systems according to the ULTraS model, an extension of the usual LTSs where the transition relation associates any source state and transition label with state reachability weight functions (like, e.g., probability distributions). This format, hence called Weight Function SOS (WFSOS), covers many known systems and their bisimulations (e.g. PEPA, TIPP, PCSP) and GSOS formats (e.g. GSOS, Weighted GSOS, Segala-GSOS, among others). The second contribution is a characterization of these systems as coalgebras of a class of functors, parametric on the weight structure. This result allows us to prove soundness of the WFSOS specification format, and that bisimilarities induced by these specifications are always congruences.Comment: In Proceedings QAPL 2014, arXiv:1406.156

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Section: Discussionmentioning

confidence: 99%

GSOS for non-deterministic processes with quantitative aspects

Miculan

Peressotti

2014

Electron. Proc. Theor. Comput. Sci.

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“…The operator α → α * was thoroughly studied in [Bre14,Bre15,BMP15,BP16] in the context of coalgebraic weak bisimulation. Its definition does not require a complete lattice order.…”

Section: Abstract Automata and Their Behaviourmentioning

confidence: 99%

“…In the setting of systems X → T F X it is obtained in terms of the initial algebra-final coalgebra coincidence [HJS07,BMSZ15]. When translated to the setting of systems with internal moves, the finite trace is given by µx.x • α : X−→ • • 0 and is calculated in the Kleisli category for the monad T F * [Bre14,Bre15]. However, this holds for coalgebras whose type monad encodes accepting states.…”

Section: Additional Remarksmentioning

confidence: 99%

“…In the coalgebraic literature [Bre14, Bre15, BP16, BMP15, Bre18, BP19] these systems are often referred to by the name of systems with internal moves. This name is motivated by the research on a unifying theory of finite behaviour for systems with internal steps [SW13,Bre14,Bre15,BMSZ15,BP16,BMP15]. They arise in a natural manner in many branches of theoretical computer science, among which are process calculi [Mil89] (labelled transition systems and their weak bisimulation) or automata theory (automata with ε-moves), to name only two.…”

Section: Introductionmentioning

confidence: 99%

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

Brengos¹

2021

Logical Methods in Computer Science

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We present a general coalgebraic setting in which we define finite and infinite behaviour with B\"uchi 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 (B\"uchi) automata, tree automata and probabilistic automata.

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“…It has been shown in [3,4,5] that from the point of view of the theory of coalgebra the systems with silent moves should be considered as coalgebras over a monadic type. This allows us to abstract away from a specific structure on labels and consider systems of the type X → T X for a monad T .…”

Section: Introductionmentioning

confidence: 99%

Lax functors and coalgebraic weak bisimulation

Brengos¹

2014

Preprint

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We generalize the work by Sobociński on relational presheaves and their connection with weak (bi)simulation for labelled transistion systems to a coalgebraic setting. We show that the coalgebraic notion of saturation studied in our previous work can be expressed in the language of lax functors in terms of existence of a certain adjunction between categories of lax functors. This observation allows us to generalize the notion of the coalgebraic weak bisimulation to lax functors. We instantiate this definition on two examples of timed systems and show that it coincides with their time-abstract behavioural equivalence. Contents1. Introduction 1 Content and organization of the paper 3 2. Basic notions 3 2.1. Coalgebras 4 2.2. Monads and their Kleisli categories 4 2.3. Coalgebras with internal moves 7 2.4. Order enriched categories 7 2.5. Coalgebras and functional simulations 8 2.6. Coalgebraic (weak) bisimulation and saturation 9 2.7. Relational presheaves 12 3. Lax functors 13 3.1. Examples and their properties 13 3.2. Change-of-base functor and its left adjoint 18 4. Weak bisimulation 24 4.1. Weak bisimulation for lax functors 24 4.2. Weak bisimulation on M -flows 28 4.3. Weak bisimulation for coalgebras revisited 30 5. Summary 30 References 31

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On Coalgebras with Internal Moves

Cited by 7 publications

References 30 publications

GSOS for non-deterministic processes with quantitative aspects

GSOS for non-deterministic processes with quantitative aspects

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

Lax functors and coalgebraic weak bisimulation

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