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Bisimulation from Open Maps
 Information and Computation
, 1994
"... An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction f ..."
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Cited by 123 (42 self)
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An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets) and labelled event structures are considered. On transition systems the abstract definition readily specialises to Milner's strong bisimulation. On event structures it explains and leads to a revision of historypreserving bisimulation of Rabinovitch and Traktenbrot, Goltz and van Glabeek. A tieup with open maps in a (pre)topos, as they appear in the work of Joyal and Moerdijk, brings to light a promising new model, presheaves on categories of pomsets, into which the usual category of labelled event structures embeds fully and faithfully. As an indication of its promise, this new presheaf model has "refinement" operators, though further work is required to justify their appropriateness and understand their relation to previous attempts. The general approach yields a logic, generalising HennessyMilner logic, which is characteristic for the generalised notion of bisimulation.
On the Expressive Completeness of the Propositional MuCalculus With Respect to Monadic Second Order Logic
, 1996
"... . Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional calculus. This expressive completeness result implies that every logic over tran ..."
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Cited by 68 (4 self)
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. Monadic second order logic (MSOL) over transition systems is considered. It is shown that every formula of MSOL which does not distinguish between bisimilar models is equivalent to a formula of the propositional calculus. This expressive completeness result implies that every logic over transition systems invariant under bisimulation and translatable into MSOL can be also translated into the calculus. This gives a precise meaning to the statement that most propositional logics of programs can be translated into the calculus. 1 Introduction Transition systems are structures consisting of a nonempty set of states, a set of unary relations describing properties of states and a set of binary relations describing transitions between states. It was advocated by many authors [26, 3] that this kind of structures provide a good framework for describing behaviour of programs (or program schemes), or even more generally, engineering systems, provided their evolution in time is disc...
Bisimulation and Open Maps
 In Proc. LICS'93, Eighth Annual Symposium on Logic in Computer Science
, 1993
"... An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from ..."
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Cited by 36 (7 self)
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An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets) and labelled event structures are considered. On transition systems the abstract definition readily specialises to Milner's strong bisimulation. On event structures it explains and leads to a revision of historypreserving bisimulation of Rabinovitch and Traktenbrot, Goltz and van Glabeek. A tieup with open maps in a (pre)topos, as they appear in the work of Joyal and Moerdijk, brings to light a promising new model, presheaves on categories of pomsets, into which the usual category of labelled event structures embeds fully and faithfully. As an indication of its promise, this new presheaf model has "refinement" operators, though further work is required to justify their appropri...
History Dependent Automata
, 2001
"... In this paper we present historydependent automata (HDautomata in brief). They are an extension of ordinary automata that overcomes their limitations in dealing with historydependent formalisms. In a historydependent formalism the actions that a system can perform carry information generated i ..."
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Cited by 32 (9 self)
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In this paper we present historydependent automata (HDautomata in brief). They are an extension of ordinary automata that overcomes their limitations in dealing with historydependent formalisms. In a historydependent formalism the actions that a system can perform carry information generated in the past history of the system. The most interesting example is calculus: channel names can be created by some actions and they can then be referenced by successive actions. Other examples are CCS with localities and the historypreserving semantics of Petri nets. Ordinary
Petri Nets and Bisimulations
 THEORETICAL COMPUTER SCIENCE
, 1995
"... Several categorical relationships (adjunctions) between models for concurrency have been established, allowing the translation of concepts and properties from one model to another. A central example is a coreflection between Petri nets and asynchronous transition systems. The purpose of the pres ..."
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Cited by 16 (7 self)
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Several categorical relationships (adjunctions) between models for concurrency have been established, allowing the translation of concepts and properties from one model to another. A central example is a coreflection between Petri nets and asynchronous transition systems. The purpose of the present paper is to illustrate the use of such relationships by transferring to Petri nets a general concept of bisimulation.
HistoryDependent Automata
 ELECTR. NOTES IN TH. COMP. SCI
, 1998
"... In this paper we present historydependent automata (HDautomata in brief). They are an extension of ordinary automata that overcomes their limitations in dealing with historydependent formalisms. In a historydependent formalism the actions that a system can perform carry information generated in ..."
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Cited by 14 (1 self)
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In this paper we present historydependent automata (HDautomata in brief). They are an extension of ordinary automata that overcomes their limitations in dealing with historydependent formalisms. In a historydependent formalism the actions that a system can perform carry information generated in the past history of the system. The most interesting example is calculus: channel names can be created by some actions and they can then be referenced by successive actions. Other examples are CCS with localities and the historypreserving semantics of Petri nets. Ordinary automata are an unsatisfactory operational model for these formalisms: infinite automata are obtained for all the systems with in nite computations, even for very simple ones; moreover, the ordinary definition of bisimulation does not apply in these cases, thus preventing the reusage of standard theories and algorithms. In this paper we show that HDautomata are an adequate model for the historydependent formalisms. We pr...
Categories in Concurrency
 Semantics and Logics of Computation, Publications of the Newton Institute
, 1997
"... These notes survey a range of models for parallel computation, including interleaving models like transition systems, synchronisation trees and languages (often called Hoare traces in this context), and models like asynchronous transition systems, event structures, pomsets and Mazurkiewicz traces wh ..."
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Cited by 5 (0 self)
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These notes survey a range of models for parallel computation, including interleaving models like transition systems, synchronisation trees and languages (often called Hoare traces in this context), and models like asynchronous transition systems, event structures, pomsets and Mazurkiewicz traces where concurrency is represented more explicitly by a form of causal independence. The presentation is unified by casting the models in a categorytheoretic framework. One aim is to use category theory to provide abstract characterisations of constructions like parallel composition valid throughout a range of different models and to provide formal means for translating between different models. The framework helps in extending the useful concept of bisimulation equivalence from its familiar situation on transition systems, to independence models where without a careful analysis even the appropriate definition of bisimulation is not clearcut. 1 Contents 1 Introduction 3 2 Transition systems 5...
Weak Bisimulation and Open Maps (Extended Abstract)
, 1999
"... A systematic treatment of weak bisimulation and observational congruence on presheaf models is presented. The theory is developed with respect to a "hiding" functor from a category of paths to observable paths. Via a view of processes as bundles , we are able to account for weak morphi ..."
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Cited by 4 (4 self)
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A systematic treatment of weak bisimulation and observational congruence on presheaf models is presented. The theory is developed with respect to a "hiding" functor from a category of paths to observable paths. Via a view of processes as bundles , we are able to account for weak morphisms (roughly only required to preserve observable paths) and to derive a saturation monad (on the category of presheaves over the category of paths). Weak morphisms may be encoded as strong ones via the Kleisli construction associated to the saturation monad. A general
A Nonwellfounded Sets Semantics for Observation Congruence over Full CCS
, 1994
"... . In the present paper we study the semantics of a minor variant of Milner's CCS process calculus. We use a compact semantic domain for processes which has been described by Aczel in [P. Aczel. Nonwellfounded Sets. Stanford University, 1988.] On the basis of the operational semantics of CC ..."
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Cited by 2 (1 self)
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. In the present paper we study the semantics of a minor variant of Milner's CCS process calculus. We use a compact semantic domain for processes which has been described by Aczel in [P. Aczel. Nonwellfounded Sets. Stanford University, 1988.] On the basis of the operational semantics of CCS we construct a semantic mapping from CCS into the domain. We prove that this mapping is fully abstract wrt. observation congruence, initial in a category of algebras, and final in a category of coalgebras. Furthermore, we give a logical characterization of the objects reached by it. 1. Introduction Observation congruence ([Mil80], [Mil89]) has become one of the most successful concepts in process algebra. It is the coarsest congruence contained in weak bisimulation equivalence, an equivalence which abstracts from invisible behaviour and is thus very intuitive. What is more, observation congruence usually differs from weak bisimulation equivalence only in the treatment of initial invisible tran...