M. C. B. Hennessy and G. D. Plotkin. A term model for CCS. In Proceedings 9th MFCS, LNCS 88, 1980.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....represents the result of input communication as an abstraction, denoting a function from values to processes. Whereas the usual models for concurrency, transition systems, labelled Petri nets and event structures and the like, accommodate early semantics for value passing directly, following [14, 7, 8], the late semantics seems accomplished most smoothly in domain theoretic settings, which readily support abstractions. Two ways seem open to extending models for concurrency to higher order features. One is to take existing models, most of these transitions systems in one disguise or another, ....

Hennessy, M., and Plotkin, G., A term model for CCS. Proc. 9th MFCS, Poland, LNCS 88, 1980.

....be turned into a labelled transition system with divergence by stipulating that, for t 2 ST1 (Act) ffl t iff Omega is a summand of t, and ffl t a i t i iff a i : t i is a summand of t. The behavioural relation over processes that we shall study in this paper is that of prebisimulation [8, 11, 6, 13] (also known as partial bisimulation [3] Definition 2.1 Let (Proc; Act; be an lts. Let Rel(Proc) denote the set of binary relations over Proc. Define the functional F : Rel(Proc) Rel(Proc) by: F (R) f(p; q) j 8a 2 Act ffl p ffl p #) q # and jj g A ....

M. Hennessy and G. Plotkin, A term model for CCS, in 9 Symposium on Mathematical Foundations of Computer Science, P. Dembi'nski, ed., vol. 88 of Lecture Notes in Computer Science, Springer-Verlag, 1980, pp. 261--274.

....of 1 we only test whether the defining constraints of the preorder hold when the only possible input and output value is v 1 , and in general in the definition of n we test the constraints for the first n values only. Here we would like to point out that this idea originally appears in [HP80]. It turns out that in our new sense and that the model is fully abstract with respect to . We will prove both these results in this paper using techniques which are similar to those used by Hennessy in the above mentioned reference [Hen81] The structure of the paper is as follows: In ....

....We also recall that the compact elements both have finite depth and width , i.e. map all but finite number of values to . These considerations motivate the following definition of value finitary strong applicative prebisimulation. This definition is a slight modification of the one given in [HP80]. Definition 4.4 [Value Finitary Strong Applicative Prebisimulation] Let AT = hCon; V al; Act; Gamma ; #i be an applicative transition system, V V al and R Con Theta Con. Then we define the V restricted extension of R, Rj V by 1. c 1 Rj V c 2 iff c 1 Rc 2 2. v 1 ; c 1 )Rj V (v 2 ; c 2 ....

M. Hennessy and G.D. Plotkin. A term model for CCS. In P. Dembi'nski, editor, 9 Symposium on Mathematical Foundations of Computer Science, volume 88 of Lecture Notes in Computer Science, pages 261--274. Springer-Verlag, 1980.

....several process description languages. In particular, when proving full abstraction results for denotational semantics based on the Scott Strachey approach [29] for CCS like languages, several preorders based on bisimulation have been considered. The interested reader is invited to consult, e.g. [13, 10, 4, 6, 17] for examples of full abstraction results with respect to bisimulation based preorders for variations on CCS. In this paper, we shall study one such bisimulation based preorder whose connections with domain theoretic models are by now well understood, viz. the prebisimulation preorder ....

....Labelled Transition Systems and Prebisimulation We begin by reviewing a variation on the model of labelled transition systems [18, 28] that takes divergence information into account, and abstracts from the operational semantics of many concurrent calculi. We refer the interested readers to, e.g. [13, 10, 22, 32] for motivation and more information on (variations on) this semantic model for reactive systems. Definition 2.1 (Labelled Transition Systems with Divergence) A labelled transition system with divergence (lts) is a quadruple (Proc; Act; where: 4 ffl Proc is a set of processes, ranged ....

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M. Hennessy and G. Plotkin, A term model for CCS, in 9 Symposium on Mathematical Foundations of Computer Science, P. Dembi'nski, ed., vol. 88 of Lecture Notes in Computer Science, Springer-Verlag, 1980, pp. 261--274.

....set of operators but C a set of channel names. We then define the general class of ( Sigma; C) domains which is a direct generalization of the standard Sigma domains introduced in [GTWW77] In fact the ( Sigma; C) domains are only a slight modification of the Natural Interpretations introduced in [HP80] and used in [HI93] Then we introduce the notion of recursively closed subsets of a process algebra. Next, in x2.3, we show how we may turn an algebraic cpo into a ( Sigma; C) domain by defining the operators on the compact elements, making sure that they are monotonic and then extending them ....

M. Hennessy and G.D. Plotkin. A term model for CCS. In P. Dembi'nski, editor, 9 th Symposium on Mathematical Foundations of Computer Science, volume 88 of Lecture Notes in Computer Science, pages 261--274. Springer-Verlag, 1980.

....denotational semantics for PAL and prove that it is fully abstract with respect to the testing preorders. The denotational model shall be given under the form of a natural interpretation. This is a slight variant of the usual algebraic semantics (see, e.g. 25, 28] and it has been introduced in [31] for dealing with languages with value passing (see, e.g. 31, 29, 35] Much of the following notation is borrowed from [29, 35] Notation 7.1 We will write x: be(x) Gamma g(x) h(x) to denote a function f which is defined by f(x) g(x) if be(x) f(x) h(x) otherwise. Let A 1 ; A 2 ; B 1 ....

....with respect to the testing preorders. The denotational model shall be given under the form of a natural interpretation. This is a slight variant of the usual algebraic semantics (see, e.g. 25, 28] and it has been introduced in [31] for dealing with languages with value passing (see, e.g. [31, 29, 35]) Much of the following notation is borrowed from [29, 35] Notation 7.1 We will write x: be(x) Gamma g(x) h(x) to denote a function f which is defined by f(x) g(x) if be(x) f(x) h(x) otherwise. Let A 1 ; A 2 ; B 1 and B 2 be sets and f j : A j Gamma B j , j = 1; 2. Let ] denote ....

M.C.B. Hennessy, G.D.Plotkin. A term model for CCS. MFCS'80, Proceedings (P. Dembinsky, Ed.), LNCS 88, pp. 261-274, Springer, 1980.

....only if (A [ A rec [ A I [ A ) E = F . Stated differently, we have obtained a complete proof system for CCS modulo observational congruence with WFAR. The proof system differs from other treatments of divergence in CCS. Walker has studied divergence sensitive bisimilarity [41] see also [22]) His basic notion is a preorder rather than an equivalence. The induced equivalence turns out to be incomparable with Milner s original notion of observational congruence. Our notion of observational congruence does neither coincide with Milner s divergence insensitive notion (denoted c ....

M. Hennessy and G.D. Plotkin. A term model for CCS. In Proceedings MFCS 80, Springer LNCS 88:261-274.

.... used for this purpose will be Abramsky s domain of synchronization trees D presented in [1] and the denotational semantics automatically generated by our methods will be guaranteed to be fully abstract with respect to the finitely observable part of the bisimulation preorder studied in, e.g. [9, 11]. Moreover, in the process of establishing the full abstraction result, we also give an algorithm, along the lines of those given in [2] to generate a complete axiomatization of the bisimulation preorder. As a byproduct of our denotational semantics, we shall be able to establish very general ....

....Def. 3.3 gives the following convergence predicate: 1) ffi #; 2) if P # and Q #, then P Q # and PkQ #; and (3) if P # then (P ) #. The reader familiar with the literature on prebisimulation over CCS like languages will have noted the similarity of this definition with those given in, e.g. [9, 7, 1]. We shall now present our non standard operational semantics for GSOS languages. As stated above, we take as our starting point the original theory developed by Bloom, Istrail and Meyer. However, in the presence of divergence information, we shall interpret negative transition formulae over ....

M. Hennessy and G. Plotkin, A term model for CCS, in 9 th Symposium on Mathematical Foundations of Computer Science, P. Dembi'nski, ed., vol. 88 of Lecture Notes in Computer Science, Springer-Verlag, 1980, pp. 261--274.

....semantics for PAL and prove that it is fully abstract with respect to the testing preorders. The denotational model shall be given under the form of a natural interpretation. This is a slight variant of the usual algebraic semantics (see, e.g. 27, 30] and it has been introduced in [33] for dealing with languages with value passing (see, e.g. 33, 31, 37] Much of the following notation is borrowed from [31, 37] Notation 7.1 Let A 1 ; A 2 ; B 1 and B 2 be sets and f i : A i Gamma B i , i = 1; 2. We let f 1 ] f 2 denote the function with functionality A 1 ] A 2 Gamma B ....

....with respect to the testing preorders. The denotational model shall be given under the form of a natural interpretation. This is a slight variant of the usual algebraic semantics (see, e.g. 27, 30] and it has been introduced in [33] for dealing with languages with value passing (see, e.g. [33, 31, 37]) Much of the following notation is borrowed from [31, 37] Notation 7.1 Let A 1 ; A 2 ; B 1 and B 2 be sets and f i : A i Gamma B i , i = 1; 2. We let f 1 ] f 2 denote the function with functionality A 1 ] A 2 Gamma B 1 ] B 2 defined by: f 1 ] f 2 ) a) f 1 (a) if a 2 A 1 ; f 2 (a) ....

M.C.B. Hennessy, G.D.Plotkin. A term model for CCS. MFCS'80, Proceedings (P. Dembinsky, Ed.), LNCS 88, pp. 261-274, Springer, 1980.

....only if (A[A rec [A I [A nf 1g) E = F . Stated differently, we have obtained a complete proof system for CCS modulo observational congruence with WFAR. The proof system differs from other treatments of divergence in CCS. Walker has studied divergence sensitive bisimilarity [41] see also [22]) His basic notion is a preorder rather than an equivalence. The induced equivalence turns out to be incomparable with Milner s original notion of observational congruence. Our notion of observational congruence does neither coincide with Milner s divergence insensitive notion (denoted c ....

M. Hennessy and G.D. Plotkin. A term model for CCS. In Proceedings MFCS 80, Springer LNCS 88:261-274.

.... 0 : p ff = p 0 p 0 Rq 0 ) In this shape the convergent weak bisimulation preorder (v WB #, no difference between may and must) can be recognized as the bisimulation preorder studied in Stirling [39] Abramsky [1] and Walker [41] the idea of which originates from Hennessy Plotkin [22]. In Bergstra, Klop Olderog [7] bisimulation semantics with explicit divergence is introduced. If I abstract from the root condition (B4) and the distinction between deadlock and successful termination (B5) in [7] their Delta bisimulation the Delta is pronounced delay and is used as a ....

M. Hennessy & G.D. Plotkin (1980): A term model for CCS. In P. Dembi'nski, editor: 9 th Symposium on Mathematical Foundations of Computer Science, Lecture Notes in Computer Science 88, Springer-Verlag, pp. 261--274.

.... Equations have been used to capture strong and weak bisimulations of CCS, both without message passing (by Hennessy and Milner, and Walker in [6, 13, 14] and with message passing (by Hennessy and Plotkin in [7]) Two main results of [7] are a complete characterization of bisimulation with divergence and a fully abstract model of CCS. Only the former result is relevant to this paper. Because of a partial order is used in the complete characterization by Hennessy and Plotkin, and is obtained through ....

.... Equations have been used to capture strong and weak bisimulations of CCS, both without message passing (by Hennessy and Milner, and Walker in [6, 13, 14] and with message passing (by Hennessy and Plotkin in [7] Two main results of [7] are a complete characterization of bisimulation with divergence and a fully abstract model of CCS. Only the former result is relevant to this paper. Because of a partial order is used in the complete characterization by Hennessy and Plotkin, and is obtained through and . However, an rule (1 1) ....

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M. Hennessy and G. Plotkin, \A Term Model for CCS", LNCS vol.88, pp.261-274, SpringerVerlag, 1980.

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Matthew C. B. Hennessy and Gordon D. Plotkin, A Term Model for CCS, Proc. 9th. MFCS (ed. P. Dembinski), LNCS, Vol. 88, pp. 261-274, Berlin: SpringerVerlag, 1980.

....from P n Q it is not possible, in general, to infer x 2 S T n x 2 S U from any finite set of statements about agents; we can not require the establishment of T n U because these are open terms and the proof system only allows the manipulation of closed terms. To overcome this problem, following [4], we introduce an infinitary proof rule: clINPUT. In short, for agents in SA, instead of considering the congruence generated by a set of axioms AX we consider the identities derivable in the proof system given in Figure 2. For any agents P; Q let AN P = Q mean that P = Q can be derived in this ....

M. Hennessy and G.D. Plotkin. A term model for CCS. In P. Dembi'nski, editor, 9 th Symposium on Mathematical Foundations of Computer Science, volume 88 of Lecture Notes in Computer Science, pages 261--274. Springer-Verlag, 1980.

....P n Q it is not possible, in general, to infer x 2 S T n x 2 S U from any finite set of statements about agents; we can not require the establishment of T n U because these are open terms and the proof system only allows the manipulation of closed terms. To overcome this problem, following [8], we introduce an infinitary proof rule: cl INPUT, a form of absorption rule for inputs: T [v=x] U [v=x] U [v=x] for every v 2 S x 2 S T x 2 S U = x 2 S U In short, for agents in SA, instead of considering the congruence generated by a set of axioms AX we consider the identities ....

M. Hennessy and G.D. Plotkin. A term model for CCS. In P. Dembi'nski, editor, 9 th Symposium on Mathematical Foundations of Computer Science, volume 88 of Lecture Notes in Computer Science, pages 261--274. SpringerVerlag, 1980.

No context found.

M. C. B. Hennessy and G. D. Plotkin. A term model for CCS. In Proceedings 9th MFCS, LNCS 88, 1980.

No context found.

M. C. B. Hennessy and G. D. Plotkin. A term model for CCS. In Proceedings 9th MFCS, LNCS 88, 1980.

No context found.

M. Hennessy and G. Plotkin. A term model for CCS. In Proceedings of the 9th International Symposium on Mathematical Foundations of Computer Science (MFCS'80), volume 88 of LNCS, pages 261--274. Springer-Verlag, 1980.

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M. Hennessy and G.D. Plotkin. A term model for CCS. In P. Dembinski, editor, 9 Symposium on Mathematical Foundations of Computer Science, volume 88 of Lecture Notes in Computer Science, pages 261--274. Springer-Verlag, 1980.

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Hennessy, M. and Plotkin, G., "A Term Model for CCS", SpringerVerlag Lecture Notes in Computer Science, vol.88, 1980.

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