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51
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 116 (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
Hereditary History Preserving Bisimulations or What is the Power of the Future Perfect in Program Logics
 Polish Academy of Sciences
, 1991
"... Contents 1 History Preserving Bisimulations on Labelled Event Structures 2 1.1 Finitary Prime Event Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Labelled Event Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 History Preserving Bisimulations ..."
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Cited by 36 (0 self)
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Contents 1 History Preserving Bisimulations on Labelled Event Structures 2 1.1 Finitary Prime Event Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.2 Labelled Event Structures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 History Preserving Bisimulations . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Relations Between History Preserving Bisimulations . . . . . . . . . . . . . . . . 5 2 History Preserving Bisimulations and Refinement 7 2.1 Refinement of Labelled Event Structures . . . . . . . . . . . . . . . . . . . . . . . 7 2.2 History Preserving Bisimulations vs Refinement . . . . . . . . . . . . . . . . . . . 8 3 Back and Forth Bisimulation on Sequential Systems 8 3.1 Unfolding transition systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.2 Unfolding versus BackandForth Bisimulation . . . . . . . . . . . . . . . . . . . 12 3.3 The Power of the Future Pe
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 36 (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
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 34 (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 33 (13 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
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 32 (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...
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.
Bisimilarity of Open Terms
, 2000
"... Traditionally, in process calculi, relations over open terms, i.e., terms with free process variables, are defined as extensions of closedterm relations: two open terms are related if and only if all their closed instantiations are related. Working in the context of bisimulation, in this paper we s ..."
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Cited by 20 (0 self)
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Traditionally, in process calculi, relations over open terms, i.e., terms with free process variables, are defined as extensions of closedterm relations: two open terms are related if and only if all their closed instantiations are related. Working in the context of bisimulation, in this paper we study a different approach; we define semantic models for open terms, socalled conditional transition systems, and define bisimulation directly on those models. It turns out that this can be done in at least two different ways, one giving rise to De Simone's formal hypothesis bisimilarity and the other to a variation which we call hypothesispreserving bisimilarity (denoted t fh and t hp, respectively). For open terms, we have (strict) inclusions t fh /t hp / t ci (the latter denoting the standard ``closed instance' ' extension); for closed terms, the three coincide. Each of these relations is a congruence in the usual sense. We also give an alternative characterisation of t hp in terms of nonconditional transitions, as substitutionclosed bisimilarity (denoted t sb). Finally, we study the issue of recursion congruence: we prove that each of the above relations is a congruence with respect to the recursion operator; however, for t ci this result holds under more restrictive conditions than for tfh and thp.]