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A Companion to Coalgebraic Weak Bisimulation for ActionType Systems ∗
"... 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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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. 1
ANALYTIC FUNCTORS AND WEAK PULLBACKS For the sixtieth birthday of Walter Tholen
"... Abstract. For accessible setvalued functors it is well known that weak preservation of limits is equivalent to representability, and weak preservation of connected limits to familial representability. In contrast, preservation of weak wide pullbacks is equivalent to being a coproduct of quotients o ..."
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Abstract. For accessible setvalued functors it is well known that weak preservation of limits is equivalent to representability, and weak preservation of connected limits to familial representability. In contrast, preservation of weak wide pullbacks is equivalent to being a coproduct of quotients of homfunctors modulo groups of automorphisms. For finitary functors this was proved by André Joyal who called these functors analytic. We introduce a generalization of Joyal’s concept from endofunctors of Set to endofunctors of a symmetric monoidal category. 1.
UNIVERSAL COALGEBRAS AND THEIR LOGICS
, 2009
"... ABSTRACT. We survey coalgebras as models of state based systems together with their global and local logics. We convey some useful intuition regarding Setfunctors which leads naturally to coalgebraic modal logic where modalities are validity patterns for the successor object of a state. 1. ..."
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ABSTRACT. We survey coalgebras as models of state based systems together with their global and local logics. We convey some useful intuition regarding Setfunctors which leads naturally to coalgebraic modal logic where modalities are validity patterns for the successor object of a state. 1.
Contents lists available at ScienceDirect
"... Information and Computation journal homepage:www.elsevier.com/locate/ic Complete sets of cooperations ..."
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Information and Computation journal homepage:www.elsevier.com/locate/ic Complete sets of cooperations
London, United Kingdom
"... The structure map turning a set into the carrier of a final coalgebra is not unique. This fact is wellknown but commonly elided. In this paper we argue that any such concrete representation of a set as a final coalgebra is potentially interesting on its own. We discuss several examples, in particul ..."
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The structure map turning a set into the carrier of a final coalgebra is not unique. This fact is wellknown but commonly elided. In this paper we argue that any such concrete representation of a set as a final coalgebra is potentially interesting on its own. We discuss several examples, in particular, we consider different coalgebra structures that turn the set of infinite streams into the carrier of a final coalgebra. After that we focus on coalgebra structures that are made up using socalled cooperations. We say that a collection of cooperations is complete for a given set X if it gives rise to a coalgebra structure that turns X into the carrier set of a subcoalgebra of a final coalgebra. Any complete set of cooperations yields a coalgebraic proof and definition principle. We exploit this fact and devise a general definition scheme for constants and functions on a set X that is parametrically in the choice of the complete set of cooperations for X. Key words: Coalgebra, coinduction, infinite data structures, hidden algebra. 1
www.elsevier.com/locate/entcs Observational Coalgebras and Complete Sets of Cooperations
"... In this paper we introduce the notion of an observational coalgebra structure and of a complete set of cooperations. We demonstrate in various example the usefulness of these notions, in particular, we show how they give rise to coalgebraic proof and definition principles. Keywords: Coalgebra, Coin ..."
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In this paper we introduce the notion of an observational coalgebra structure and of a complete set of cooperations. We demonstrate in various example the usefulness of these notions, in particular, we show how they give rise to coalgebraic proof and definition principles. Keywords: Coalgebra, Coinduction, infinite data structures, Hidden Algebra.
Hybrid Logic with the Difference Modality for Generalisations of Graphs
"... We discuss recent work generalising the basic hybrid logic with the difference modality to any reasonable notion of transition. This applies equally to both subrelational transitions such as monotone neighbourhood frames or selection function models as well as those with more structure such as Marko ..."
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We discuss recent work generalising the basic hybrid logic with the difference modality to any reasonable notion of transition. This applies equally to both subrelational transitions such as monotone neighbourhood frames or selection function models as well as those with more structure such as Markov chains and alternating temporal frames. We provide a generic canonical cutfree sequent system and a terminating proofsearch strategy for the fragment without the difference modality but including the global modality. Keywords: Global Modality, Difference Modality, Coalgebraic Semantics, Cutfree Sequent System