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Tile Transition Systems as Structured Coalgebras
 Fundamentals of Computation Theory, volume 1684 of LNCS
, 1999
"... . The aim of this paper is to investigate the relation between two models of concurrent systems: tile rewrite systems and coalgebras. Tiles are rewrite rules with side effects which are endowed with operations of parallel and sequential composition and synchronization. Their models can be described ..."
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. The aim of this paper is to investigate the relation between two models of concurrent systems: tile rewrite systems and coalgebras. Tiles are rewrite rules with side effects which are endowed with operations of parallel and sequential composition and synchronization. Their models can be described as monoidal double categories. Coalgebras can be considered, in a suitable mathematical setting, as dual to algebras. They can be used as models of dynamical systems with hidden states in order to study concepts of observational equivalence and bisimilarity in a more general setting. In order to capture in the coalgebraic presentation the algebraic structure given by the composition operations on tiles, coalgebras have to be endowed with an algebraic structure as well. This leads to the concept of structured coalgebras, i.e., coalgebras for an endofunctor on a category of algebras. However, structured coalgebras are more restrictive than tile models. Those models which can be presented as st...
Coalgebraic Symbolic Semantics
"... The operational semantics of interactive systems is usually described by labeled transition systems. Abstract semantics (that is defined in terms of bisimilarity) is characterized by the final morphism in some category of coalgebras. Since the behaviour of interactive systems is for many reasons in ..."
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The operational semantics of interactive systems is usually described by labeled transition systems. Abstract semantics (that is defined in terms of bisimilarity) is characterized by the final morphism in some category of coalgebras. Since the behaviour of interactive systems is for many reasons infinite, symbolic semantics were introduced as a mean to define smaller, possibly finite, transition systems, by employing symbolic actions and avoiding some sources of infiniteness. Unfortunately, symbolic bisimilarity has a different “shape” with respect to ordinary bisimilarity, and thus the standard coalgebraic characterization does not work. In this paper, we introduce its coalgebraic models.
Coalgebra Morphisms Subsume Open Maps
, 1999
"... We relate two abstract notions of bisimulation, induced by open maps and by coalgebras morphisms, respectively. We show that open maps correspond to coalgebra morphisms for a suitable chosen endofunctor in a category of many sorted sets. This demonstrates that the notion of openmaps bisimilarity is ..."
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We relate two abstract notions of bisimulation, induced by open maps and by coalgebras morphisms, respectively. We show that open maps correspond to coalgebra morphisms for a suitable chosen endofunctor in a category of many sorted sets. This demonstrates that the notion of openmaps bisimilarity is of essentially coalgebraic nature. We nd moreover characterizations of subcategories of coalgebras corresponding to some relevant model categories: category of presheaves is isomorphic to the subcategory of consistent coalgebras with lax cohomomorphisms; a suitably chosen subcategory of many sorted algebras is equivalent to the full subcategory of presheaves preserving nite products.
A coalgebraic theory of reactive systems
"... In this report we study the connection between two well known models for interactive systems. Reactive Systems à la Leifer and Milner allow to derive an interactive semantics from a reduction semantics guaranteeing, semantics (bisimilarity). Universal Coalgebra provides a categorical framework where ..."
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In this report we study the connection between two well known models for interactive systems. Reactive Systems à la Leifer and Milner allow to derive an interactive semantics from a reduction semantics guaranteeing, semantics (bisimilarity). Universal Coalgebra provides a categorical framework where bisimilarity can be characterized as final semantics, i.e., as the unique morphism to the final coalgebra. Moreover, if lifting a coalgebra to a structured setting is possible, then bisimilarity is compositional with respect to the lifted structure. Here we show that for every reactive system we can build a coalgebra. Furthermore, if bisimilarity is compositional in the reactive system, then we can lift this coalgebra to a structured coalgebra. 1
A coalgebraic theory of reactive systems
, 1999
"... In this report we study the connection between two well known models for interactive systems. Reactive Systems à la Leifer and Milner allow to derive an interactive semantics from a reduction semantics guaranteeing, semantics (bisimilarity). Universal Coalgebra provides a categorical framework where ..."
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Cited by 1 (0 self)
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In this report we study the connection between two well known models for interactive systems. Reactive Systems à la Leifer and Milner allow to derive an interactive semantics from a reduction semantics guaranteeing, semantics (bisimilarity). Universal Coalgebra provides a categorical framework where bisimilarity can be characterized as final semantics, i.e., as the unique morphism to the final coalgebra. Moreover, if lifting a coalgebra to a structured setting is possible, then bisimilarity is compositional with respect to the lifted structure. Here we show that for every reactive system we can build a coalgebra. Furthermore, if bisimilarity is compositional in the reactive system, then we can lift this coalgebra to a structured coalgebra.
Structured Coalbegras and Minimal HDAutomata for the πCalculus
, 2000
"... The coalgebraic framework developed for the classical process algebras, and in particular its advantages concerning minimal realizations, does not fully apply to the picalculus, due to the constraints on the freshly generated names that appear in the bisimulation. In this paper we propose to model ..."
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The coalgebraic framework developed for the classical process algebras, and in particular its advantages concerning minimal realizations, does not fully apply to the picalculus, due to the constraints on the freshly generated names that appear in the bisimulation. In this paper we propose to model the transition system of the πcalculus as a coalgebra on a category of name permutation algebras and to define its abstract semantics as the final coalgebra of such a category. We show that permutations are sufficient to represent in an explicit way fresh name generation, thus allowing for the definition of minimal realizations. We also link the coalgebraic semantics with a slightly improved version of history dependent (HD) automata, a model developed for verification purposes, where states have local names and transitions are decorated with names and name relations. HDautomata associated with agents with a bounded number of threads in their derivatives are finite and can be actually minimized. We show that the bisimulation relation in the coalgebraic context corresponds to the minimal HDautomaton.
www.elsevier.com/locate/entcs GReactive Systems as Coalgebras
"... The semantics of process calculi has traditionally been specified by labelled transition systems (LTSs), but with the development of name calculi it turned out that definitions employing reduction semantics are sometimes more natural. Reactive Systems à la Leifer and Milner allow to derive from a re ..."
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The semantics of process calculi has traditionally been specified by labelled transition systems (LTSs), but with the development of name calculi it turned out that definitions employing reduction semantics are sometimes more natural. Reactive Systems à la Leifer and Milner allow to derive from a reduction semantics definition an LTS equipped with a bisimilarity relation which is a congruence. This theory has been extended to GReactive Systems by Sassone and Sobocinki in order to properly handle structural equivalence. Universal Coalgebra provides a categorical framework where bisimilarity can be characterized as final semantics, i.e., each LTS can be mapped to a minimal realization identifying bisimilar states. Moreover, it is often possible to lift coalgebras to an algebraic setting (yielding bialgebras by Turi and Plotkin or, slightly more generally, structured coalgebras by Corradini, Heckel and Montanari) with the property that bisimilarity is compositional with respect to the lifted structure. The existence of minimal realizations is of theoretical interest, but it is even more of practical interest whenever LTSs are employed for finite state verification. In this paper we show that for every GReactive System we can build a coalgebra. Furthermore, if bisimilarity is compositional in the Reactive System, then we can lift this coalgebra to a structured coalgebra. Keywords: coalgebra Process calculus, labelled transition system, reactive systems, Greactve systems, universal 1