D. Sangiorgi and R. Milner. The problem of iWeak Bisimulation up toj. In W.R. Cleveland, editor, Proc. CONCUR '92, volume 630 of Lecture Notes in Computer Science, pages 3246. Springer Verlag, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the fact that, by Denition 5. 1(6) a located ambient that can create a new located ambient cannot be in a wait state and, therefore, cannot receive migration messages (which would make it into a forwarder) Some proofs are carried out using the technique of ibarbed expansion up to expansionj [13]. Denition 5.6 A net A is in normal form if it cannot perform an administrative reduction. Lemma 5.7 For every A there is a normal form A such that 1. A A , and A ffl = A by means of a sequence of administrative reductions. Moreover, the normal form A is unique up to j, in the ....

D. Sangiorgi and R. Milner. The problem of iWeak Bisimulation up toj. Proc. CONCUR '92, LNCS 630, pages 3246. Springer Verlag, 1992. 14

....Le, ground bisimilarity coincides with early, late, and open bisimilarities [24] All these relations are congruences and imply barbed congruence. In the technical part of this paper we shall need a means to count the number of silent moves performed by a process in order to use up to techniques [28, 25]. The expansion relation [3] written . is an asymmetric variant of such that P . Q holds if P Q, and Q has at least as many moves as P . Denition 3 (expansion) A relation S on processes is an expansion if P S Q implies: 1. whenever P Gamma P 0 , and bn( fn(Q) there exists Q ....

D. Sangiorgi and R. Milner. The problem of iWeak Bisimulation up toj. In W.R. Cleveland, editor, Proc. CONCUR '92, volume 630 of Lecture Notes in Computer Science, pages 3246. Springer Verlag, 1992.

....for weak internal transitions. Theorem 5.9 (operational correspondence of [ on weak interactions) Gamma P and Gamma is closed. Gamma . For composing the results we actually need an asymmetric version of , along the style of the expansion relation [38]. 28 Corollary 5.10 (adequacy of [ Suppose LHO . Gamma P and Gamma is closed. Then LHO . P a ioe L a , for all a. A corollary of Theorems 3.7 and 5.9 and Corollary 5.10 is the full abstraction for barbed bisimulation. Corollary 5.11 Suppose LHO . Gamma P ; Q and ....

D. Sangiorgi and R. Milner. The problem of iWeak Bisimulation up toj. In W.R. Cleveland, editor, Proc. CONCUR '92, volume 630 of Lecture Notes in Computer Science, pages 3246. Springer Verlag, 1992.

....of a bisimulation relation is achieved up to bisimilarity itself. The portability of this technique onto weak bisimilarities (where a special action, called silent action, is distinguished from the others and partially ignored in the bisimilarity clause) has been studied by Milner and Sangiorgi [SM92]. Two special cases of the up to context technique had been previously put forward: In [Cau90] Caucal 4 denes a notion of self bisimulation in the setting of BPA processes (they can be viewed as the processes generated by a context free grammar) which allows him to eliminate common prexes and ....

.... respectful function constructors) The reason is that the soundness of some basic techniques for weak bisimilarities presents a few rather delicate points whose fragility might be enhanced in combinations of techniques (see for instance the study of iweak bisimulations up to weak bisimilarityj in [SM92]) We believe that our proof techniques could be very advantageous in higher order calculi like CHOCS [Tho90] or Higher Order calculus [San92] i.e. calculi in which terms can be exchanged in a communication. For instance, a few rather involved proofs in [San92] dealing with the Higher Order ....

D. Sangiorgi and R. Milner. The problem of iWeak Bisimulation up toj. In W.R. Cleveland, editor, Proc. CONCUR '92, volume 630 of Lecture Notes in Computer Science, pages 3246. Springer Verlag, 1992.

....if P i L Q then P and Q are well typed w.r.t. the same type environment. Lemma 5.6 Let P and Q be complete discreet processes. If P i L Q, then there is Delta s.t. Delta; LD P; Q. Proof techniques for the labeled bisimilarities of the ordinary calculus, like ibisimulation up to expansionj [SM92], can be adapted to bisimulation under receptiveness; the proof schema is the same. An instance of this technique is bisimulation up to j, where the occurrences of R in the clauses of Denition 5.3 are replaced by j R j (the composition of the three relations) In Subsection 5.1 we shall extend ....

D. Sangiorgi and R. Milner. The problem of iWeak Bisimulation up toj. In W.R. Cleveland, editor, Proc. CONCUR '92, volume 630 of Lecture Notes in Computer Science, pages 3246. Springer Verlag, 1992.

....to it. Lemma B.5 Suppose P; Q 2 a . Then . P u c Q implies a . P u c Q. Proof: a is a subcalculus of , therefore all contexts of are also contexts of a . Xi We sometimes write P to mean that P a , for some a. B.0. 7 The expansion relation The expansion relation [AKH92, SM92] written . is an asymmetric variant of which takes into account the number of actions performed by processes. Thus, P . Q holds if P Q and Q has at least as many moves as P . De nition B.6 (expansion) A relation R on calculus processes is an expansion if P R Q implies: 1. If P ....

D. Sangiorgi and R. Milner. The problem of iWeak Bisimulation up toj. In W.R. Cleveland, editor, Proc. CONCUR '92, volume 630 of Lecture Notes in Computer Science, pages 3246. Springer Verlag, 1992.

....barbed congruence) The equality can be established by exhibiting an appropriate bisimulation relation. The proof is fairly simple (the two processes are almost identical) one can use standard reasoning as for systems with an inductive structure ( 9, chapter 6] the up to expansion technique [18] can be used to reduce the size of the bisimulation relation the proofs of the running examples in [18] are similar to that of (12) Acknowledgements. The author would like to thank Clioe Jones and Benjamin Pierce for several useful discussions during the early stages of this study. This ....

.... The proof is fairly simple (the two processes are almost identical) one can use standard reasoning as for systems with an inductive structure ( 9, chapter 6] the up to expansion technique [18] can be used to reduce the size of the bisimulation relation the proofs of the running examples in [18] are similar to that of (12) Acknowledgements. The author would like to thank Clioe Jones and Benjamin Pierce for several useful discussions during the early stages of this study. This research has been supported by France T#l#com, CtiCnet 95 1B 182, iMod#lisation de Syst#mes Mobilesj. SC1ha; b; ....

D. Sangiorgi and R. Milner. The problem of iWeak Bisimulation up toj. In W.R. Cleveland, editor, Proc. CONCUR '92, volume 630 of Lecture Notes in Computer Science, pages 3246. Springer Verlag, 1992.

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