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143
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 405 (43 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 304 (36 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.”
Bisimulation for Labelled Markov Processes
 INFORMATION AND COMPUTATION
, 1997
"... In this paper we introduce a new class of labelled transition systems  Labelled Markov Processes  and define bisimulation for them. Labelled Markov processes are ..."
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Cited by 204 (25 self)
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In this paper we introduce a new class of labelled transition systems  Labelled Markov Processes  and define bisimulation for them. Labelled Markov processes are
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 136 (13 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 106 (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...
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 59 (3 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
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 50 (11 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
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 49 (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
A Logical Characterization of Bisimulation for Labeled Markov Processes
"... This paper gives a logical characterization of probabilistic bisimulation for Markov processes introduced in [5]. ffl Bisimulation can be characterized by a very weakmodal logic. The most striking feature is that one has no negation or any kind of negative proposition. ffl Bisimulation can be charac ..."
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Cited by 43 (12 self)
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This paper gives a logical characterization of probabilistic bisimulation for Markov processes introduced in [5]. ffl Bisimulation can be characterized by a very weakmodal logic. The most striking feature is that one has no negation or any kind of negative proposition. ffl Bisimulation can be characterized by several inequivalent logics; we report five in this paper and there are surely many more. ffl We do not need any finite branching assumption yetthere is no need of infinitary conjunction. ffl We give an algorithm for deciding bisimilarity of finite state systems which constructs a formula that witnesses the failure of bisimulation.