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76
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.
Presheaf Models for Concurrency
, 1999
"... In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their wo ..."
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Cited by 45 (19 self)
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In this dissertation we investigate presheaf models for concurrent computation. Our aim is to provide a systematic treatment of bisimulation for a wide range of concurrent process calculi. Bisimilarity is defined abstractly in terms of open maps as in the work of Joyal, Nielsen and Winskel. Their work inspired this thesis by suggesting that presheaf categories could provide abstract models for concurrency with a builtin notion of bisimulation. We show how
Refinement of Actions and Equivalence Notions for Concurrent Systems
 Acta Informatica
, 1998
"... This paper combines and extends the material of [GGa/c/d/e], except for the part in [GGc] on refinement of transitions in Petri nets and the discussion of TCSPlike parallel composition in [GGe]. An informal presentation of some basic ingredients of this paper appeared as [GGb]. Among others, th ..."
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Cited by 45 (1 self)
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This paper combines and extends the material of [GGa/c/d/e], except for the part in [GGc] on refinement of transitions in Petri nets and the discussion of TCSPlike parallel composition in [GGe]. An informal presentation of some basic ingredients of this paper appeared as [GGb]. Among others, the treatment of action refinement in stable and nonstable event structures is new. The research reported here was supported by Esprit project 432 (METEOR), Esprit Basic Research Action 3148 (DEMON), Sonderforschungsbereich 342 of the TU Munchen, ONR grant N0001492J1974 and the Human Capital and Mobility Cooperation Network EXPRESS (Expressiveness of Languages for Concurrency). Contents
DYNAMIC CONGRUENCE vs. PROGRESSING BISIMULATION for CCS
 Fundamenta Informaticae
, 1992
"... Weak Observational Congruence (woc) defined on CCS agents is not a bisimulation since it does not require two states reached by bisimilar computations of woc agents to be still woc, e.g. ff:ø:fi:nil and ff:fi:nil are woc but ø:fi:nil and fi:nil are not. This fact prevent us from characterizing CCS s ..."
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Cited by 36 (12 self)
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Weak Observational Congruence (woc) defined on CCS agents is not a bisimulation since it does not require two states reached by bisimilar computations of woc agents to be still woc, e.g. ff:ø:fi:nil and ff:fi:nil are woc but ø:fi:nil and fi:nil are not. This fact prevent us from characterizing CCS semantics (when ø is considered invisible) as a final algebra, since the semantic function would induce an equivalence over the agents that is both a congruence and a bisimulation. In the paper we introduce a new behavioural equivalence for CCS agents, which is the coarsest among those bisimulations which are also congruences. We call it Dynamic Observational Congruence because it expresses a natural notion of equivalence for concurrent systems required to simulate each other in the presence of dynamic, i.e. run time, (re)configurations. We provide an algebraic characterization of Dynamic Congruence in terms of a universal property of finality. Furthermore we introduce Progressing Bisimulatio...
Action Structures
, 1992
"... Action structures are proposed as a variety of algebra to underlie concrete models of concurrency and interaction. An action structure is equipped with composition and product of actions, together with two other ingredients: an indexed family of abstractors to allow parametrisation of actions, a ..."
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Cited by 35 (1 self)
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Action structures are proposed as a variety of algebra to underlie concrete models of concurrency and interaction. An action structure is equipped with composition and product of actions, together with two other ingredients: an indexed family of abstractors to allow parametrisation of actions, and a reaction relation to represent activity. The eight axioms of an action structure make it an enriched strict monoidal category; however, the work is presented algebraically rather than in category theory. The notion of action structure is developed mathematically, and examples are studied ranging from the evaluation of expressions to the statics and dynamics of Petri nets. For algebraic process calculi in particular, it is shown how they may be defined by a uniform superposition of process structure upon an action structure specific to each calculus. This allows a common treatment of bisimulation congruence. The theory of action structures emphasizes the notion of effect; that ...
Modelling concurrent computations: from contextual Petri nets to graph grammars
, 2000
"... Graph grammars (or graph transformation systems), originally introduced as a generalization of string grammars, can be seen as a powerful formalism for the specification of concurrent and distributed systems, which properly extends Petri nets. The idea is that the state of a distributed system can b ..."
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Cited by 35 (14 self)
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Graph grammars (or graph transformation systems), originally introduced as a generalization of string grammars, can be seen as a powerful formalism for the specification of concurrent and distributed systems, which properly extends Petri nets. The idea is that the state of a distributed system can be naturally represented (at a suitable level of abstraction) as a graph and local state transformations can be expressed as production applications. With the aim of consolidating the foundations of the concurrency theory for graph transformation systems, the thesis extends to this more general setting some fundamental approaches to the semantics coming from Petri net theory. More specifically, focusing on the socalled double pushout (dpo) algebraic approach to graph rewriting, the thesis provides graph transformation systems with truly concurrent semantics based on (concatenable) processes and on a Winskel’s style unfolding construction, as well as with more abstract semantics based on event structures and domains. The first part of the thesis studies two generalizations of Petri nets, already known in the literature, which reveal a close relationship with graph transformation systems, namely contextual nets (also called nets with read, activator or test arcs) and inhibitor nets (or nets with inhibitor arcs). Extending Winskel’s seminal work on safe nets, the truly concurrent semantics of contextual nets is given via a chain
Gates accept concurrent behavior
 In Proc. 34th Ann. IEEE Symp. on Foundations of Comp. Sci
, 1993
"... We represent concurrent processes as Boolean propositions or gates, cast in the role of acceptors of concurrent behavior. This properly extends other mainstream representations of concurrent behavior such as event structures, yet is defined more simply. It admits an intrinsic notion of duality that ..."
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Cited by 32 (16 self)
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We represent concurrent processes as Boolean propositions or gates, cast in the role of acceptors of concurrent behavior. This properly extends other mainstream representations of concurrent behavior such as event structures, yet is defined more simply. It admits an intrinsic notion of duality that permits processes to be viewed as either schedules or automata. Its algebraic structure is essentially that of linear logic, with its morphisms being consequencepreserving renamings of propositions, and with its operations forming the core of a natural concurrent programming language. 1
Models for NamePassing Processes: Interleaving and Causal
 In Proceedings of LICS 2000: the 15th IEEE Symposium on Logic in Computer Science (Santa Barbara
, 2000
"... We study syntaxfree models for namepassing processes. For interleaving semantics, we identify the indexing structure required of an early labelled transition system to support the usual picalculus operations, defining Indexed Labelled Transition Systems. For noninterleaving causal semantics we de ..."
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Cited by 24 (3 self)
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We study syntaxfree models for namepassing processes. For interleaving semantics, we identify the indexing structure required of an early labelled transition system to support the usual picalculus operations, defining Indexed Labelled Transition Systems. For noninterleaving causal semantics we define Indexed Labelled Asynchronous Transition Systems, smoothly generalizing both our interleaving model and the standard Asynchronous Transition Systems model for CCSlike calculi. In each case we relate a denotational semantics to an operational view, for bisimulation and causal bisimulation respectively. We establish completeness properties of, and adjunctions between, categories of the two models. Alternative indexing structures and possible applications are also discussed. These are first steps towards a uniform understanding of the semantics and operations of namepassing calculi.
Ready Simulation, Bisimulation, and the Semantics of CCSLike Languages
, 1993
"... The questions of program comparison  asking when two programs are equal, or when one is a suitable substitute for another  are central in the semantics and verification of programs. It is not obvious what the definitions of comparison should be for parallel programs, even in the relatively sim ..."
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Cited by 23 (3 self)
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The questions of program comparison  asking when two programs are equal, or when one is a suitable substitute for another  are central in the semantics and verification of programs. It is not obvious what the definitions of comparison should be for parallel programs, even in the relatively simple case of core languages for concurrency, such as the kernel language of Milner's CCS. We introduce some criteria for judging notions of program comparison. Our basic notion is that of a congruence: two programs are equivalent with respect to a language L and a set of observations O iff they cannot be distinguished by any observation in O in any context of L. Bisimulation, the notion of program equivalence ordinarily used with CCS, is finer than CCS congruence: there are two programs which are not bisimilar, but cannot be told apart by CCS contexts. We explore the possibility of making bisimulation into a congruence. We CCS is defined by a set of structured operational rules. We introduc...