A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127(2):164185, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....branching structure, one may think of a non deterministic computation as a tree where the nodes correspond to points where a non deterministic choice is made. The computation paths can then be embedded in the tree as branches. An abstract account of bisimulation has been given for such a setting [JNW96] where a model for concurrency is presented as a category C with a given subcategory of paths: P , C . In any such setting, one can define a notion of bisimulation. In familiar cases such as transition systems and event structures, this definition leads to familiar notions of bisimulation. One ....

....and co fibrations over a category of sets of labels; co fibration model substitution, or relabelling, and fibrations model inverse relabelling and restriction. Furthermore, because a category P is embedded in the presheaf category P, the presheaf category comes with a notion of bisimulation [JNW96], and weak bisimulation [FCW99] Presheaf models have been given to CCS like languages [CW96] a value passing version of CCS [Win96] and the p calculus [CSW97] An approach towards a theory of domains for concurrency based on presheaf models is presented in [CFW98] Presheaf models differ from ....

Andr'e Joyal, Mogens Nielsen, and Glynn Winskel. Bisimulation from open maps. Information and Computation, 127:164--185, 1996.

....of concurrency. When two concurrent systems are bisimilar, known properties are readily transferred from one system to the other. For every notion of concurrency or for every notion of process algebra, there has been a di#erent notion of bisimulation and frequently several competing notions. In [7], Joyal, Nielsen and Winskel proposed the notion of span of open maps in an attempt to understand the various equivalence notions for concurrency in an abstract categorical setting. They also showed that this abstract definition of bisimilarity captures the strong bisimulation relation of Milner ....

....developing bisimulation equivalence for hybrid systems. There has been very recent work characterizing the the notion of bisimulation for dynamical and control systems [12, 15] In [4] we have further shown that this equivalence relation is captured by the abstract bisimulation relation of [7]. The goal of this paper is to combine known notions of bisimulation for discrete systems with recently developed notions for continuous systems and develop novel but natural notions of bisimulation for hybrid systems. Furthermore, we show that this notion is also captured in the framework of [7] ....

[Article contains additional citation context not shown here]

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127(2):164--185, 1996.

....t with source s and target s # labelled by a is denoted t : s s # . Arnold is ambiguous about whether the condition on # is required. It means that there is only one transition with a given label between two states, and is sometimes expressed by saying that T is a subset of S S (e.g. [JNW96]) In the sequel we will be mainly concerned with variants of the category of (directed) graphs, Graph. This category has as objects the parallel pairs of mappings G : G 1 which specify the set of edges G 1 and the set of vertices (or nodes) G 0 , and the source and target mappings, s G and ....

....G # is called path lifting if whenever e # : #(g) g # is an an a labelled edge in G # with source #(g) and target g # , then there is an (a labelled) edge e : g g 1 in G which satisfies #(e) e # and hence #(g 1 ) g # . Path lifting morphisms have been considered by several authors (see [JNW96] or [BF00] and references there) Clearly, a graph isomorphism is path lifting and path lifting morphisms compose, so there is a category of labelled graphs and path lifting morphisms. It is an easy exercise to show that for labelled graphs G, G # a relation r : R ## G 0 # 0 on their node sets ....

[Article contains additional citation context not shown here]

A. Joyal, M. Nielson and G. Winskel. Bisimulation from open maps. Information and Computation, 127:164--185, 1996.

.... of bisimulation are by now well established [13] Category theory has been successfully used to understand and compare the multitude of models for concurrency by Winskel and Nielsen [22] Related efforts include the categorically inspired framework for comparing models of computation in [12] In [6], Joyal, Nielsen and Winskel proposed the notion of span of open maps in an attempt to understand the various equivalence notions for concurrency in an abstract categorical setting. They also showed that this abstract defi nition of bisimilarity captures the strong bisimulation relation of Milner ....

.... language, include the coalgebraic approach of [5,17] In this paper we propose a new equivalence relation for dynamical and control systems (see also [15,19] that we call bisimulation and further show that this equivalence relation is captured by the abstract bisimulation relation of JNW [6]. This extends the latter abstract framework to the continuous domains in control and systems theory. In this paper, our main focus, besides introducing a new equivalence relation for dynamical and control systems, is to establish a unification result for bisimulation of discrete and continuous ....

[Article contains additional citation context not shown here]

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127(2):164-185, 1996.

.... of bisimulation are by now well established [10] Category theory has been successfully used to understand and compare the multitude of models for concurrency by Winskel and Nielsen [16] Related e#orts include the categorically inspired framework for comparing models of computation in [9] In [2], Joyal, Nielsen and Winskel proposed the notion of span of open maps in an attempt to understand the various equivalence notions for concurrency in an abstract categorical setting. They also showed that this abstract definition of bisimilarity captures the strong bisimulation relation of Milner ....

.... language, include the coalgebraic approach of [1, 13] In this paper we propose a new equivalence relation for dynamical and control systems (see also [12] that we call bisimulation and further show that this equivalence relation is captured by the abstract bisimulation relation of JNW [2]. This extends the latter abstract framework to the continuous domain. In this paper, our main focus, besides introducing a new equivalence relation for dynamical and control systems, is to establish a unification result for bisimulation of discrete and continuous systems. We postpone the ....

[Article contains additional citation context not shown here]

M. Nielsen A. Joyal and G. Winskel. Bisimulation from open maps. Information and Computation, 127(2):164--185, 1996.

.... for timed BPP in a full standard form [9] Surprisingly, polynomial time complexity of history preserving bisimilarity on BPP can be contrasted with the EXPTIME completeness on finite state systems (finite 1 safe nets) 21] Similarly, decidability of hereditary history preserving bisimilarity [4, 22] on BPP, proved in [13] can be contrasted with undecidability on finite 1 safe nets shown by Jurdzi nski in [23] We start by Section 2 containing basic definitions and then we outline our algorithm in Section 3. The algorithm works for BPP processes in standard form, similarly as in [9] A ....

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127:164--185, 1996.

....of the operational semantics. The context of this work is an ongoing effort to unify models of concurrency and their notions of bisimulation into one framework, a domain theory based on presheaf models and open map bisimulation. The endeavor was initiated by Joyal, Nielsen and Winskel in [15] and pursued further in two PhD theses [3, 11] and a number of papers including [6, 20, 5, 4, 13, 21, 9, 12, 7] Presheaf models are instantiations of the following situation: Let P be a small category in which objects are viewed as computation path shapes with morphisms saying how paths can be ....

....= P , Set] of presheaves over P in which each object can be seen as a set of computation paths from P glued together by identifying subpaths to form a process with non deterministic branching. The presheaf category comes with a built in notion of bisimulation, obtained from open maps [15]. Further, it can be characterised abstractly as the free colimit completion of P, and so the class of path categories can be naturally assembled as the objects of a 2 category called Cocont with arrows colimit preserving functors between the associated presheaf categories, and with natural ....

[Article contains additional citation context not shown here]

Andre Joyal, Mogens Nielsen, and Glynn Winskel. Bisimulation from open maps. Information and Computation, 127(2):164--185, June 1996.

No context found.

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127:164--185, 1996.

....2 as above, the inclusion holds i# for all (#, P) program contexts C, we have the implication C(t 1 ) #. 4. 3 Simulation The path semantics does not capture enough of the branching behaviour of processes to characterise bisimilarity (for that, the presheaf semantics is needed, see [11, 19]) As an example, the processes # # and # have the same denotation, but are clearly not bisimilar. However, using Hennessy Milner logic we can link path equivalence to simulation. In detail, we consider the fragment of Hennessy Milner logic given by possibility and finite conjunctions; it ....

....gives instead a set of realisers , saying how a path may be realised. This extra information can be used to obtain refined versions of the proofs of soundness and adequacy, giving hope of extending the full abstraction result to a characterisation of bisimilarity, possibly in terms of open maps [11]. Replacing the exponential by a lifting comonad yields a model A# of a#ne linear logic and an a#ne version of HOPLA, again with a fully abstract path semantics [20] The tensor operation of A# can be understood as a simple parallel composition of event structures [17] Thus, the a#ne ....

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127:164--185, 1996.

....[14] in which processes denote mappings from computation paths to sets of realisers saying how each computation path may be realised. This extra structure allows the incorporation of complete branching information, and the corresponding notion of process equivalence is a form of bisimulation [26]. The two approaches are variations on a common idea: that a process denotes a form of characteristic function in which the truth values are sets of realisers. A path set may be viewed as a special presheaf that yields at most one realiser for each path. The study of presheaf models for ....

....the nondeterministic branching of a process and a presheaf semantics can support equivalences such as forms of bisimulation which are sensitive to the branching behaviour of processes. Though here our understanding of the role of open maps and open map bisimulation, intrinsic to presheaf models [26], is very incomplete. The presheaf semantics helps expose a range of possible pseudo comonads with which to interpret P [39] 6.2 Powerdomains The adjunction between Lin and Cts, key to our semantics of HOPLA, determines a monad, the monad of the Hoare powerdomain [51] The adjunction ....

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127:164--185, 1996.

....to be confused with a failure generated by tell operation. except that notion of observability (a process P being observable at channel ) is augmented by taking the store into account. Presently, we are studying the application of the categorical framework of bisimulation in terms of open maps [JNW96] to the CCP model. Preliminary results show that the equivalence we obtain from this framework coincides with the obvious strong bisimulation derived from the weak bisimulation in [MPSS95] Therefore, this notion of behavioral equivalence seems to be a promising starting point in our quest for an ....

Andr Joyal, Mogens Nielsen, and Glynn Winskel. Bisimulation from open maps. Information and Computation, 127(2):164--185, 15 June 1996.

....es for a typical path p the set X(p) of computation paths of shape p, and acts on e : p q to give a function X(e) saying how paths of shape q restrict to paths of shape p. In this way a presheaf can model the nondeterministic branching of a process. For more information of presheaf models, see [14, 4]. A presheaf category has all colimits and so in particular all sums (coproducts) for any set I , the sum i2I X i of presheaves X i over P has a contribution i2I X i (p) the disjoint union of sets, at p 2 P. The empty sum is the presheaf with empty contribution at each p. In process ....

....with constantly maps F : P Q for 2 A di erent from , applied to the denotation of u. 2. 4 Rooted Presheaves and Operational Semantics The category P has an initial element , given by the empty colimit, and a presheaf over P is called rooted if it has a singleton contribution at see [14]. As an example, the denotation of :t with t closed is rooted. We can decompose any presheaf X over P as a sum of rooted presheaves i2X( X i , each X i a presheaf over P. This is the key to the correspondence between the denotational semantics and the operational semantics of Sect. 4. ....

[Article contains additional citation context not shown here]

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127:164-185, 1996.

....set # , the new root being #; the restriction maps are extended so that restriction to sends elements to #. map from X to Y in P is sent to its obvious extension from #X# #Y # . Presheaves that to within isomorphism can be obtained as images under are called rooted [12]. Proposition 2.1 Any presheaf Y in has a decomposition as a sum of rooted presheaves Y = # i#Y (#) where, for i Y (#) the presheaf Y i in P is, to within isomorphism, given as Y i (p) x # Y (p) Y p )x = i where p is the unique arrow p in P# . Intuitively, ....

....a 2 comonad on Lin with A# as its coKleisli category. The comonad ( # has turned the model of linear logic Lin into a model A# of affine linear logic (where the tensor unit is terminal) 2.3. Bisimulation Bisimulation between presheaves is derived from the notion of open map between presheaves [11, 12]. A morphism h : X Y , between presheaves X,Y over P, is open iff for all morphisms e : p q in , any commuting square (on the left below) can be split into two commuting triangles (on the right) z Y That the square commutes means that the path h#x in Y can be ....

[Article contains additional citation context not shown here]

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127:164--185, 1996.

....Basic Research in Computer Science, Centre of the Danish National Research Foundation. Introduction We seek a category theoretic axiomatic account of bisimulation as studied in concurrency, for instance by Milner [16] There have been several category theoretic approaches to bisimulation [8, 10]. One of them, initiated by Joyal, Nielsen, and Winskel [10] uses the notion of open map to de ne functional bisimulation, then de nes a bisimulation to be a span of epimorphic open maps. That work has only partly been axiomatic: they developed a particular construction, namely the presheaf ....

....National Research Foundation. Introduction We seek a category theoretic axiomatic account of bisimulation as studied in concurrency, for instance by Milner [16] There have been several category theoretic approaches to bisimulation [8, 10] One of them, initiated by Joyal, Nielsen, and Winskel [10], uses the notion of open map to de ne functional bisimulation, then de nes a bisimulation to be a span of epimorphic open maps. That work has only partly been axiomatic: they developed a particular construction, namely the presheaf construction, and studied properties of the 2 category ....

[Article contains additional citation context not shown here]

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127:164-185, 1996.

....on the category of transition systems, in line with their being operations of saturation. Corresponding monads on the category of synchronisation trees are derived by composing the coreflection from synchronisation trees to transition systems with the monads on transition systems. The paper [13] shows how to generalise strong bisimulation to other classes of models presented as categories via spans of open maps. Once we have strong bisimulation in place for a particular category of models, given analogues of Milner s operations as monads we can define the corresponding weak bisimulation ....

....addressed afresh for each new process language. The contribution of this paper is a study of a systematic way to define weak bisimulation and observational congruence on presheaf models. Presheaf models have been shown to include traditional models like synchronisation trees and event structures [13] along with their notion of bisim ulation, to be related by powerful preservation properties associated with colimit preserving functors [9] and to form a domain theory for bisimulation [23, 7, 6] in which a wide range of, possibly higher order, process languages can receive a denotational ....

[Article contains additional citation context not shown here]

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127(2):164--185, 1996.

No context found.

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127(2):164185, 1996.

No context found.

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127(2):164--185, 1996.

No context found.

Andre Joyal, Mogens Nielsen, and Glynn Winskel. Bisimulation from open maps. Information and Computation, 127(2):164--185, 1996.

No context found.

Andre Joyal, Mogens Nielsen, and Glynn Winskel. Bisimulation from open maps. Information and Computation, 127(2):164--185, 1996.

No context found.

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127:164--185, 1996.

No context found.

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127:164--185, 1996.

No context found.

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127(2):164--185, 1996.

No context found.

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127:164-185, 1996.

No context found.

A. Joyal, M. Nielsen, and G. Winskel. Bisimulation from open maps. Information and Computation, 127:164--185, 1996.

No context found.

A. JOYAL, M. NIELSEN & G. WINSKEL (1996): Bisimulation from open maps. Information and Computation 127(2), pp. 164--185.

First 50 documents  Next 50

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC