D. Sangiorgi and R. Milner. The problem of weak bisimulation up-to. In Proc. CONCUR'92, volume 630 of LNCS, pages 32-46. Springer, 1992. A revised version has appeared as a technical report.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....s hl j ; k j i Then, P h vi Qh vi. Proof. For simplicity, we omit the obligations on types on the coinductive de nition of . We prove that the relation S= f(P hwi; Qhwi) e w = w 1 . wm with w j : h l j ; k j i; j 2 1. mg is a bisimilarity up to expansion and up to context [SM92, San96] Let s consider all the possible actions of P h e wi and Qh e wi. 1. The case P h e wi shl;ki P 0 h f w 0 i with f w 0 = e w [ hl; ki is straightforward. Similarly for Qh e wi shl;ki Q 0 h f w 0 i. 2. If Qh e wi s hl j ;k j i Q 0 h f w 0 i, with f w 0 = e ....

D. Sangiorgi and R. Milner. The Problem of \Weak Bisimulation up to". In R. Cleaveland, ed, Proceedings of CONCUR '92, volume 630 of LNCS, pages 32-46. Springer, 1992.

....automatic tactics. In Section 3, we have achieved this by proving bisimulation obligations in separate theorems. In Section 4, we have exploited compositionality of observation equivalence. Here, we discuss the application of up to techniques that have been proposed by Sangiorgi and Milner in [19] in order to reduce the size of the relations. That is, instead of showing that a relation R is a bisimulation, one chooses some suitable S and proves that S R S 1 is a bisimulation. Observe that the size of S R S 1 . can be far larger than the size of S and R. The theory of up ....

D. Sangiorgi and R. Milner. The problem of weak bisimulation up-to. In Proc. CONCUR'92, volume 630 of LNCS, pages 32-46. Springer, 1992. A revised version has appeared as a technical report.

....be formulated by the user, and a (possibly large) number of simple and uniform checks that can be performed more or less automatically by the prover when provided with suitable proof procedures. A strategy of this kind is o ered by observation equivalence (or weak bisimilarity, see, for instance, [4,12,11]) when following its de nition: exhibit a relation containing as a pair the system and its speci cation, and prove that it is a bisimulation. Conceptually, the dicult part is to exhibit the relation, while proving that the relation is indeed a bisimulation reduces to a (usually large) number of ....

....(usually large) number of simple checks of the form for each derivative there exists a matching derivative . 4) When using a theorem prover, one should try to divide proofs into smaller sub problems. In order to reduce the size of a bisimulation, various up to proof techniques have been proposed [12,11]. In this paper, we apply bisimulations up to expansion, thereby considerably reducing the size of the proof when compared to standard bisimulations. Cache coherence is a major problem in hardware design, and has been extensively studied in the literature (see, for instance, 2,13] Certain cache ....

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D. Sangiorgi and R. Milner. The problem of weak bisimulation up-to. In Proc. CONCUR'92, volume 630 of LNCS, pages 32-46. Springer, 1992. A revised version, \Techniques of weak bisimulation up to", has appeared as a technical report.

....approach to this problem, inspired by [3] Appendix A Congruence with respect to Recursion Congruence of with respect to the operators of STC follows the lines of [24] except for recursion. In order to prove congruence with respect to recursion we use a notion of bisimulation up to [37]. We only consider closed expressions P 2 STP . Once we have shown for closed recX:E and recX:F that E c F implies recX:E c recX:F , Definition 2.9 assures that this implication also holds for arbitrary expressions. Let S be a binary relation on STP . A sequence (R 1 ; ....

D. Sangiorgi and R. Milner. The problem of 'weak bisimulation up to'. In Proceedings CONCUR 92, Springer LNCS 630:32-46, 1992.

....and guarantees that no case is forgotten. The strengths and weaknesses of the approach are discussed. 1 Introduction Observation equivalence (or weak bisimilarity) is a natural notion of behavioural equivalence; it has been extensively studied and applied in the literature (see, for instance, [Mil89,MS92,San95]) There exist two general ways of showing that a system is observationally equivalent to its speci cation. One, semantically oriented, way is to follow the de nition: exhibit a relation containing as a pair the system and its speci cation, and prove that it is a bisimulation. Conceptually, the ....

....equivalence. In our third example we were able to replace the ABP channels by one place bu ers. Without this the bisimulation would have been unmanageable. Furthermore though we have not used them there exist various up to techniques that can be exploited to reduce the size of the relations [MS92,San95]. Up to techniques combine the direct approach with algebraic reasoning. Dealing with data structures. Although our approach does not require to master a proof system for bisimulation, it still requires a lot of expertise in theorem proving, as usually the systems to be veri ed manipulate data. ....

R. Milner and D. Sangiorgi. The problem of weak bisimulation up-to. In Proc. CONCUR'92, volume 630 of LNCS. Springer, 1992.

....A process is closed if it does not contain free variables. Otherwise it is open. For the semantics of the calculus we adopt a labelled transition system. In contrast to reduction semantics [Mil91] this allows us to use labelled forms of bisimulation and to use the associated proof techniques [MS92]. Process transitions (in the early style) are of the form P Gamma P 0 , where is given by : b)ah vi j ah vi j : b)ah vi denotes the output of the values v on the name a, where b are those channels among the names of v which are private to the sender process; ah vi ....

....bisimilarity is not a congruence in general, it is preserved by all the ways the calculus combinators are used in the encoding. The bisimulation proof technique can be made more powerful by combining it with up to techniques, like up to expansion, up to context, or up to injective substitutions [Mil89, MS92, San95b]. Expansion is an asymmetric variant of bisimulation taking into account the number of internal steps performed by the processes [AKH92] We write P Q if P expands Q, i.e. P Q but P performs more internal steps than Q. A bisimulation up to expansion abstracts from these administrative ....

R. Milner and D. Sangiorgi. The problem of weak bisimulation up-to. In Proc. CONCUR'92, volume 630 of LNCS. Springer, 1992.

....by using the characterisation of and for open expression given in Appendix C. Congruence of c with respect to the operators of STC follows the lines of [24] except for recursion. In order to prove congruence with respect to recursion we use a notion of bisimulation up to [37]. We only consider closed expressions P 2 STP . Once we have shown for closed recX:E and recX:F that E c F implies recX:E c recX:F , Definition 2.9 assures that this implication also holds for arbitrary expressions. Let S be a binary relation on STP . A sequence (R 1 ; ....

D. Sangiorgi and R. Milner. The problem of 'weak bisimulation up to'. In Proceedings CONCUR 92, Springer LNCS 630:32-46, 1992.

....A process is closed if it does not contain free variables. Otherwise it is open. For the semantics of the calculus we adopt a labelled transition system. In contrast to reduction semantics [Mil91] this allows us to use labelled forms of bisimulation and to use the associated proof techniques [MS92]. Process transitions (in the early style) are of the form P Gamma P 0 , where is given by : b)ah vi j ah vi j : b)ah vi denotes the output of the values v on the name a, where b are those channels among the names of v which are private to the sender process; ah vi ....

....even though early bisimilarity is not preserved by arbitrary summation, it is preserved by guarded summation, which suffices in our case. The bisimulation proof technique can be made more powerful by combining it with up to techniques, like up to expansion and up to injective substitutions [Mil89,MS92,San95b] (expansion is an asymmetric variant of bisimulation taking into account the number of internal steps performed by the processes [AKH92] 4 Interpreting CIA in the calculus The calculus interpretation of CIA is given by the rules in Tables 2 and 3 at the end of this paper. The storage is ....

R. Milner and D. Sangiorgi. The problem of weak bisimulation up-to. In Proc. CONCUR'92, volume 630 of LNCS. Springer, 1992.

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D. Sangiorgi and R. Milner. The problem of weak bisimulation up-to. In Proc. CONCUR'92, volume 630 of LNCS, pages 32-46. Springer, 1992. A revised version has appeared as a technical report.

No context found.

D. Sangiorgi and R. Milner. The problem of \weak bisimulation up to". In W. R. Cleaveland, editor, Proceedings of CONCUR'92, volume 630 of LNCS, pages 32-46. Springer-Verlag, 1992.

No context found.

D. Sangiorgi and R. Milner. The problem of \weak bisimulation up to". In W. R. Cleaveland, editor, Proceedings of CONCUR'92, volume 630 of LNCS, pages 32-46. Springer-Verlag, 1992.

No context found.

Davide Sangiorgi and Robin Milner. The problem of \weak bisimulation up to". In Proceedings of CONCUR '92, volume 630 of Lecture Notes in Computer Science, pages 32-46. Springer-Verlag, 1992.

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D. Sangiorgi and R. Milner. The problem of \weak bisimulation up to". In W. R. Cleaveland, editor, Proceedings of CONCUR'92, volume 630 of Lecture Notes in Computer Science, Stony Brook, New York, 24-27August 1992. SpringerVerlag.

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