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A Syntactical Approach to Weak (Bi)Simulation for Coalgebras
, 2002
"... In [19] Rutten introduced the notion of weak bisimulations and weak bisimilarity for coalgebras of the functor F (X) = X+O. In the present paper I will introduce a notion of weak bisimulation for coalgebras based on the syntax of their functors for a large class of functors. I will show that my defi ..."
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Cited by 7 (1 self)
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In [19] Rutten introduced the notion of weak bisimulations and weak bisimilarity for coalgebras of the functor F (X) = X+O. In the present paper I will introduce a notion of weak bisimulation for coalgebras based on the syntax of their functors for a large class of functors. I will show that my definition does not only coincide with the definition from [19], but with the definition for labelled transition systems as well. The approach includes a definition of weak bisimulation for Kripke structures, which might be of interest in its own right.
A Companion to Coalgebraic Weak Bisimulation for ActionType Systems
, 2009
"... We propose a coalgebraic definition of weak bisimulation for classes of coalgebras obtained from bifunctors in the category Set. Weak bisimilarity for a system is obtained as strong bisimilarity of a transformed system. The particular transformation consists of two steps: First, the behavior on acti ..."
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Cited by 5 (1 self)
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We propose a coalgebraic definition of weak bisimulation for classes of coalgebras obtained from bifunctors in the category Set. Weak bisimilarity for a system is obtained as strong bisimilarity of a transformed system. The particular transformation consists of two steps: First, the behavior on actions is lifted to behavior on finite words. Second, the behavior on finite words is taken modulo the hiding of internal or invisible actions, yielding behavior on equivalence classes of words closed under silent steps. The coalgebraic definition is validated by two correspondence results: one for the classical notion of weak bisimulation of Milner, another for the notion of weak bisimulation for generative probabilistic transition systems as advocated by Baier and Hermanns.
Weak Bisimulation for ActionType Coalgebras
"... A coalgebraic definition of weak bisimulation is proposed for a class of coalgebras obtained from bifunctors in Set. Weak bisimilarity for a system is obtained as strong bisimilarity of a transformed system. The transformation consists of two steps: First, the behaviour on actions is expanded to beh ..."
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Cited by 3 (1 self)
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A coalgebraic definition of weak bisimulation is proposed for a class of coalgebras obtained from bifunctors in Set. Weak bisimilarity for a system is obtained as strong bisimilarity of a transformed system. The transformation consists of two steps: First, the behaviour on actions is expanded to behaviour on finite words. Second, the behaviour on finite words is taken modulo the hiding of invisible actions, yielding behaviour on equivalence classes of words closed under silent steps. The coalgebraic definition is justified by two correspondence results, one for the classical notion of weak bisimulation of Milner and another for the notion of weak bisimulation for generative probabilistic transition systems as advocated by Baier and Hermanns.
Generic Process Algebra: A Programming Challenge
"... Abstract: Emerging interaction paradigms, such as serviceoriented computing, and new technological challenges, such as exogenous component coordination, suggest new roles and application areas for process algebras. This, however, entails the need for more generic and adaptable approaches to their d ..."
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Cited by 3 (3 self)
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Abstract: Emerging interaction paradigms, such as serviceoriented computing, and new technological challenges, such as exogenous component coordination, suggest new roles and application areas for process algebras. This, however, entails the need for more generic and adaptable approaches to their design. For example, some applications may require similar programming constructs coexisting with different interaction disciplines. In such a context, this paper pursues a research programme on a coinductive rephrasal of classic process algebra, proposing a clear separation between structural aspects and interaction disciplines. A particular emphasis is put on the study of interruption combinators defined by natural corecursion. The paper also illustrates the verification of their properties in an equational and pointfree reasoning style as well as their direct encoding in Haskell.
An Approach to Computable Coalgebras based on Recursive Functions ∗
, 2005
"... This paper proposes a notion of computable coalgebras based on numbered sets and recursive functions similar to the notion of computable algebra. A model that is final for the category of computable coalgebras is constructed. An investigation of the computability of the final computable coalgebra mo ..."
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This paper proposes a notion of computable coalgebras based on numbered sets and recursive functions similar to the notion of computable algebra. A model that is final for the category of computable coalgebras is constructed. An investigation of the computability of the final computable coalgebra motivates the use of partial structure maps. So a notion of computable coalgebra with partial structure map is developed. It is shown that the final model in the partial case has better computability properties than the final model in the total case. ∗The author acknowledges the suport by grants from the DFG within the PhD Programme GK 334 ”Specification of discrete processes and systems of processes by operational models and logic”. 1 1
Weak Bisimulation for ActionType
"... We propose a coalgebraic definition of weak bisimulation for a class of coalgebras obtained from bifunctors in Set. Weak bisimilarity for a system is obtained as strong bisimilarity of a transformed system. The transformation consists of two steps: First, the behaviour on actions is expanded to beha ..."
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We propose a coalgebraic definition of weak bisimulation for a class of coalgebras obtained from bifunctors in Set. Weak bisimilarity for a system is obtained as strong bisimilarity of a transformed system. The transformation consists of two steps: First, the behaviour on actions is expanded to behaviour on finite words. Second, the behaviour on finite words is taken modulo the hiding of invisible actions, yielding behaviour on equivalence classes of words closed under silent steps. The coalgebraic definition is justified by two correspondence results, one for the classical notion of weak bisimulation of Milner and another for the notion of weak bisimulation for generative probabilistic transition systems as advocated by Baier and Hermanns. Key words: system, coalgebra, bisimulation, weak bisimulation, labelled transition system, generative probabilistic transition system 1
(Extended Abstract) Abstract
"... We propose a coalgebraic definition of weak bisimulation for a class of coalgebras obtained from bifunctors over the category Set. Weak bisimilarity for a system is obtained as strong bisimilarity of a transformed system. The transformation consists of two steps: First, the behaviour on actions is e ..."
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We propose a coalgebraic definition of weak bisimulation for a class of coalgebras obtained from bifunctors over the category Set. Weak bisimilarity for a system is obtained as strong bisimilarity of a transformed system. The transformation consists of two steps: First, the behaviour on actions is expanded to behaviour on finite words. Second, the behaviour on finite words is taken modulo the hiding of invisible actions, yielding behaviour on equivalence classes of words closed under silent steps. The coalgebraic definition is justified by two correspondence results, one for the classical notion of weak bisimulation of Milner and another for the notion of weak bisimulation for generative probabilistic transition systems as advocated by Baier and Hermanns.