Bialgebras for structural operational semantics: An introduction

Klin, Bartek

doi:10.1016/j.tcs.2011.03.023

Cited by 73 publications

(111 citation statements)

References 21 publications

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“…Another approach to more powerful recursive definition principles are abstract operational rules (see [27] for an overview). It has been shown that certain rule formats define operations on the rational fixpoint [13,32], and it should be investigated whether a similar theory can be developed based on the LFF.…”

Section: Discussionmentioning

confidence: 99%

A New Foundation for Finitary Corecursion

Milius

Pattinson

Wißmann

2016

Lecture Notes in Computer Science

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Abstract. This paper contributes to a theory of the behaviour of "finite-state" systems that is generic in the system type. We propose that such systems are modeled as coalgebras with a finitely generated carrier for an endofunctor on a locally finitely presentable category. Their behaviour gives rise to a new fixpoint of the coalgebraic type functor called locally finite fixpoint (LFF). We prove that if the given endofunctor preserves monomorphisms then the LFF always exists and is a subcoalgebra of the final coalgebra (unlike the rational fixpoint previously studied by Adámek, Milius and Velebil). Moreover, we show that the LFF is characterized by two universal properties: 1. as the final locally finitely generated coalgebra, and 2. as the initial fg-iterative algebra. As instances of the LFF we first obtain the known instances of the rational fixpoint, e.g. regular languages, rational streams and formal power-series, regular trees etc. And we obtain a number of new examples, e.g. (realtime deterministic resp. non-deterministic) context-free languages, constructively S-algebraic formal power-series (and any other instance of the generalized powerset construction by Silva, Bonchi, Bonsangue, and Rutten) and the monad of Courcelle's algebraic trees.

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Section: Discussionmentioning

confidence: 99%

A New Foundation for Finitary Corecursion

Milius

Pattinson

Wißmann

2016

Lecture Notes in Computer Science

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“…See [23] for an overview of this topic. In the remainder of this paper, we assume a fixed signature Σ with associated free monad T , and a Set endofunctor F representing the type of behaviour.…”

Section: Bialgebraic Operational Semanticsmentioning

confidence: 99%

“…This provides enough structure to prove at this general level that bisimilarity is a congruence. By instantiating the theory to concrete instances, one can then obtain congruence formats for systems such as probabilistic automata, weighted transition systems and streams-see [23] for an overview. Another advantage of abstract GSOS is that bisimulation up to context is "compatible" [34,33], providing a sound enhancement of the bisimulation proof method which can be combined with other compatible enhancements such as bisimulation up to bisimilarity [39,32].…”

Section: Introductionmentioning

confidence: 99%

Structural congruence for bialgebraic semantics

Rot¹,

Bonsangue²

2016

Journal of Logical and Algebraic Methods in Programming

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It was observed by Turi and Plotkin that structural operational semantics can be studied at the level of universal coalgebra, providing specification formats for well-behaved operations on many different types of systems. We extend this framework with non-structural assignment rules which can express, for example, the syntactic format for structural congruences proposed by Mousavi and Reniers. Our main result is that the operational model of such an extended specification is well-behaved, in the sense that bisimilarity is a congruence and that bisimulation-up-to techniques are sound.

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“…Putting it yet differently, a reactive T-algebra is a δ-bialgebra for the given δ [12] (see also [18]). …”

Section: Reactive T-algebras and T-automatamentioning

confidence: 99%

Towards a Coalgebraic Chomsky Hierarchy

Goncharov¹,

Milius²,

Silva³

2014

Lecture Notes in Computer Science

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Abstract. The Chomsky hierarchy plays a prominent role in the foundations of theoretical computer science relating classes of formal languages of primary importance. In this paper we use recent developments on coalgebraic and monadbased semantics to obtain a generic notion of a T-automaton, where T is a monad, which allows the uniform study of various notions of machines (e.g. finite state machines, multi-stack machines, Turing machines, valence automata, weighted automata). We use the generalized powerset construction to define a generic (trace) semantics for T-automata, and we show by numerous examples that it correctly instantiates for some known classes of machines/languages captured by the Chomsky hierarchy. Moreover, our approach provides new generic techniques for studying expressivity power of various machine-based models.

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Bialgebras for structural operational semantics: An introduction

Cited by 73 publications

References 21 publications

A New Foundation for Finitary Corecursion

A New Foundation for Finitary Corecursion

Structural congruence for bialgebraic semantics

Towards a Coalgebraic Chomsky Hierarchy

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