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80
Universal coalgebra: a theory of systems
, 2000
"... In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certa ..."
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Cited by 298 (31 self)
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In the semantics of programming, nite data types such as finite lists, have traditionally been modelled by initial algebras. Later final coalgebras were used in order to deal with in finite data types. Coalgebras, which are the dual of algebras, turned out to be suited, moreover, as models for certain types of automata and more generally, for (transition and dynamical) systems. An important property of initial algebras is that they satisfy the familiar principle of induction. Such a principle was missing for coalgebras until the work of Aczel (NonWellFounded sets, CSLI Leethre Notes, Vol. 14, center for the study of Languages and information, Stanford, 1988) on a theory of nonwellfounded sets, in which he introduced a proof principle nowadays called coinduction. It was formulated in terms of bisimulation, a notion originally stemming from the world of concurrent programming languages. Using the notion of coalgebra homomorphism, the definition of bisimulation on coalgebras can be shown to be formally dual to that of congruence on algebras. Thus, the three basic notions of universal algebra: algebra, homomorphism of algebras, and congruence, turn out to correspond to coalgebra, homomorphism of coalgebras, and bisimulation, respectively. In this paper, the latter are taken
Relations in Concurrency
"... The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the seman ..."
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Cited by 263 (33 self)
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The theme of this paper is profunctors, and their centrality and ubiquity in understanding concurrent computation. Profunctors (a.k.a. distributors, or bimodules) are a generalisation of relations to categories. Here they are first presented and motivated via spans of event structures, and the semantics of nondeterministic dataflow. Profunctors are shown to play a key role in relating models for concurrency and to support an interpretation as higherorder processes (where input and output may be processes). Two recent directions of research are described. One is concerned with a language and computational interpretation for profunctors. This addresses the duality between input and output in profunctors. The other is to investigate general spans of event structures (the spans can be viewed as special profunctors) to give causal semantics to higherorder processes. For this it is useful to generalise event structures to allow events which “persist.”
Deriving Bisimulation Congruences for Reactive Systems
 In Proc. of CONCUR 2000, 2000. LNCS 1877
, 2000
"... . The dynamics of reactive systems, e.g. CCS, has often been de ned using a labelled transition system (LTS). More recently it has become natural in de ning dynamics to use reaction rules  i.e. unlabelled transition rules  together with a structural congruence. But LTSs lead more naturally to beha ..."
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Cited by 116 (14 self)
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. The dynamics of reactive systems, e.g. CCS, has often been de ned using a labelled transition system (LTS). More recently it has become natural in de ning dynamics to use reaction rules  i.e. unlabelled transition rules  together with a structural congruence. But LTSs lead more naturally to behavioural equivalences. So one would like to derive from reaction rules a suitable LTS. This paper shows how to derive an LTS for a wide range of reactive systems. A label for an agent a is de ned to be any context F which intuitively is just large enough so that the agent Fa (\a in context F ") is able to perform a reaction. The key contribution of this paper is a precise de nition of \just large enough", in terms of the categorical notion of relative pushout (RPO), which ensures that bisimilarity is a congruence when sucient RPOs exist. Two examples  a simpli ed form of action calculi and termrewriting  are given, for which it is shown that su cient RPOs indeed exist. The thrust of thi...
Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach
, 1998
"... . The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a ..."
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Cited by 75 (15 self)
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. The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving Borel probability measures. Under reasonable conditions, generalized probabilistic bisimilarity can be characterized categorically. Application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation. Keywords. Bisimulation, probabilistic transition system, coalgebra, ultrametric space, Borel measure, final coalgebra. 1 Introduction For discrete probabilistic transition systems the notion of probabilistic bisimilarity of Larsen and Skou [LS91] is regarded as the basic process equivalence. The definition was given for reactive systems. However, Van Glabbeek, Smolka and Steffen s...
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 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
A Presheaf Semantics of ValuePassing Processes
, 1996
"... This paper investigates presheaf models for process calculi with value passing. Denotational semantics in presheaf models are shown to correspond to operational semantics in that bisimulation obtained from open maps is proved to coincide with bisimulation as defined traditionally from the operat ..."
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Cited by 33 (18 self)
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This paper investigates presheaf models for process calculi with value passing. Denotational semantics in presheaf models are shown to correspond to operational semantics in that bisimulation obtained from open maps is proved to coincide with bisimulation as defined traditionally from the operational semantics. Both "early" and "late" semantics are considered, though the more interesting "late" semantics is emphasised. A presheaf model and denotational semantics is proposed for a language allowing process passing, though there remains the problem of relating the notion of bisimulation obtained from open maps to a more traditional definition from the operational semantics.
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 29 (8 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
A Relational Model of NonDeterministic Dataflow
 In CONCUR'98, volume 1466 of LNCS
, 1998
"... . We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits ..."
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Cited by 28 (13 self)
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. We recast dataflow in a modern categorical light using profunctors as a generalisation of relations. The well known causal anomalies associated with relational semantics of indeterminate dataflow are avoided, but still we preserve much of the intuitions of a relational model. The development fits with the view of categories of models for concurrency and the general treatment of bisimulation they provide. In particular it fits with the recent categorical formulation of feedback using traced monoidal categories. The payoffs are: (1) explicit relations to existing models and semantics, especially the usual axioms of monotone IO automata are read off from the definition of profunctors, (2) a new definition of bisimulation for dataflow, the proof of the congruence of which benefits from the preservation properties associated with open maps and (3) a treatment of higherorder dataflow as a biproduct, essentially by following the geometry of interaction programme. 1 Introduction A fundament...