J.A. Bergstra, J.W. Klop and E.R. Olderog. Readies and failures in the algebra of communicating processes. SIAM Journal of Computing, 17(6):11341177, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....by Hoare etal in [BHR84, Hoa84] for finite transition systems it coincides with the notion of testing equivalence proposed by Hennessy and de Nicola. The notion of readiness equivalence can be seen as the dual of failures equivalence and was originally put forward by Bergstra, Klop, and Olderog [BKO88] 22 Definition 3.16 For any process p, define failures(p) f(w; X) j 9p ; 8a 2 X : p Gamma g; readies(p) f(w; X) j 9p Gamma ( a 2 Xg: Processes p and q are failures equivalent, written p f q, iff failures(p) failures(q) Processes p and q are readiness ....

J.A. Bergstra, J.W. Klop, and E.-R. Olderog. Readies and failures in the algebra of communicating processes. SIAM J. on Comput., 17:1134--1177, 1988.

...., regular CCS with replaced by the internal choice operator Phi, and give it an axiomatic semantics by means of an equationally based proof system. We prove that it is sound and complete with respect to the readiness preorder. The proof system is a slight modification of the system introduced in [BKO88]. However in that reference only a sub language consisting of recursion free terms of ACP is considered. The logical characterization gives us an interesting and strong proof technique for proving properties of the behavioural preorder. Like in [AH92] we use it to prove that the preorder is ....

....(q 2 ) Der(a; Stbw (q 1 q 2 ) 4.3 The Proof System In this section we introduce a proof system to reason about process behaviour. The proof system consists of a set of equations, Figure 2, and an inference system, Figure 3. The equations are a slight modification of those introduced in [BKO88] due to a different language as in that reference a subset of recursive free processes of ACP is considered. Furthermore the proof system is almost the same as for the must testing preorder [Hen88] with the following differences. ffl The (in)equations (X Y ) Phi Z = X Phi Z) Y Phi Z) ....

J.A. Bergstra, J.W. Klop, and E.-R. Olderog. Readies and failures in the algebra of communicating processes. SIAM Journal on Computing, 17(6):1134--1177, 1988.

....soundness to the reader. Before proving this completeness theorem, we introduce some auxiliary de nitions and results. De nition 4.7. A term P is saturated if for each pair of derivations P R with b 2 initials(R) we have R R with Q R R The following lemma stems from [2]. Lemma 4.8. If P and Q is saturated, then Q with R Q 9 De nition 4.9. A normal form P is strongly saturated if: 1. P is saturated; 2. if P = AC a i :P i [ 1] then the term P i is strongly saturated, for every i 2 I . Axioms R1 R3 play a crucial role in the proof of the ....

....(x a: y z) y (x a:y) to those for bisimulation equivalence (cf. Table 2) and we are currently working on the details of such a proof. The crux of the argument is a proof to the e ect that the suggested inequations are sucient to convexly saturate each process term, in the sense of [2]. We have also obtained irredundancy results for the axioms systems for ready simulation, simulation, trace and language equivalence. These will be presented in the full version of this paper, together with a characterization of the expressive power of BCCS with pre x iteration. Acknowledgements: ....

J. Bergstra, J. W. Klop, and E.-R. Olderog, Readies and failures in the algebra of communicating processes, SIAM J. Comput., 17 (1988), pp. 1134-1177.

....For expressions of this form it is easy to establish that p 0 = PW q 0 , p 0 q 0 . Using the soundness of the axiom employed, and the completeness of TB T PW for , it follows that T PW p = p 0 = q 0 = q. For F and R (as well as B) a proof is given in Bergstra, Klop Olderog [11] by means of graph transformations. A similar proof for RT can be found in Baeten, Bergstra Klop [6] This method, applied to semantics O, requires the definition of a class IH of finite process graphs that contains at least all finite process trees, and a binary relation O ; IH Theta ....

.... x = 0 = y and hence the law follows from the third and fourth axiom of Table 2. In the second, observe that I(p) 6= 0 iff p has the form bq r with b 2 Act. Hence the law can be reformulated as a(bx u) a(cy v) a(bx cy u v) A process graph g 2 j G is called history unambiguous [11] if any two paths from the root to the same node give rise to the same trace, i.e. if for ; 0 2 paths(g) one has end( end( 0 ) T ( T ( 0 ) The history or trace T (s) of a node s in such a graph g is defined as T ( for an 64 The linear time branching time spectrum I ....

[Article contains additional citation context not shown here]

J.A. Bergstra, J.W. Klop & E.-R. Olderog (1988): Readies and failures in the algebra of communicating processes. SIAM Journal on Computing 17(6), pp. 1134--1177.

....[25] Section 3 also establishes that for any calculus in this format, the well known failure preorder is a substitutive. These results generalize and somehow explain similar results that have been obtained previously for a large number of individual calculi in De Simone s format (see for instance [10, 4]) Section 4 studies certain trace and failure preorders in the presence of internal actions. The main results of this section are that the testing preorders of [11, 14] and also a preorder that is related to the failure semantics with fair abstraction of unstable divergence of [3] are ....

....that refine completed trace equivalence. For several individual De Simone calculi a full abstractness result has been established in the literature which says that the so called failure preorder is the coarsest substitutive preorder which refines the completed trace preorder (see for instance [10, 4]) Below it will be shown that the failure preorder is substitutive for any De Simone calculus. The full abstraction result then follows for any calculus which is sufficiently expressive to distinguish between terms that are not related by the failure preorder. Definition 3.5 (Failure preorder) ....

J.A. Bergstra, J.W. Klop, and E.-R. Olderog. Readies and failures in the algebra of communicating processes. SIAM Journal on Computing, 17(6):1134--1177, 1988.

....the failure semantics is fully abstract, i.e. correct and complete, with respect to the trace semantics if and only if we have infinitely many internal actions. Similar full abstraction studies have been carried out by, e.g. De Bakker and De Vink [BV96, Chapter 17] Bergstra, Klop, and Olderog [BKO88], Horita [Hor93] Main [Mai87] and Rutten [Rut88] This paper builds on their work. The rest of this paper is organized as follows. In Section 1, we introduce the language. For this language a labelled transition system is given in Section 2. Based on this labelled transition system, a trace ....

....one. Apart from the statement variables, all the constructions of the language are used in the contexts constructed in the proof of Theorem 6.5 (cf. Definition 6.3 and Lemma 6.4) The statement variables, which allow us to specify recursion, are crucial for the results of Subsection 6.2. In [BV96, BKO88, Rut88] sequential composition instead of prefixing is used. Also restriction and renaming are present in the language studied in [BKO88] We are confident that the main results of the present paper also hold if we replace prefixing by sequential composition and add restriction and renaming. 2 Labelled ....

[Article contains additional citation context not shown here]

J.A. Bergstra, J.W. Klop, and E.-R. Olderog. Readies and Failures in the Algebra of Communicating Processes. SIAM Journal on Computing, 17(6):1134--1177, December 1988.

....proving this completeness theorem, we introduce some auxiliary definitions and results. Definition 4.8 A term P is saturated if for each pair of derivations P a Q b Q 0 and P a R with b 2 initials(R) we have R b R 0 with Q 0 R R 0 . The following lemma stems from [3]. Lemma 4.9 If P R Q and P a P 0 and Q is saturated, then Q a Q 0 with P 0 R Q 0 . Definition 4.10 A normal form P is strongly saturated if: 1. P is saturated; 2. if P = AC P i2I a i :P i [ 1] then the term P i is strongly saturated, for every i 2 I. Axioms R1 R3 ....

....by adding the laws in Table 7 to those for bisimulation equivalence (cf. Table 2) and we are currently working on the details of such a proof. The crux of the argument is a proof to the effect that the suggested inequations are sufficient to convexly saturate each process term, in the sense of [3]. F1 a: x y) a:x a: y z) F2 a:a (x y) a:a x a:a (y z) F3 a:a x a a: x y) F4 a (x y a: y z) a (x a: y z) y RS2 a x a (x a:y) Table 7: Axioms for Failures We have also obtained irredundancy results for the axioms systems for ready ....

J. Bergstra, J. W. Klop, and E.-R. Olderog, Readies and failures in the algebra of communicating processes, SIAM J. Comput., 17 (1988), pp. 1134-- 1177.

....distinctive than the De Simone format. By characterizing trace congruence by a specialized (bi)simulation one can classify (restricting to image finite transition system specifications) the various formats: completed trace congruence for De Simone format corresponds to failure equivalence j F [Sim84, BKO88], for GSOS it corresponds to 2 3 bisimulation equivalence 2 3 [BIM88, LS89] while for the tyft format it corresponds to 2 nested simulation equivalence 2 [GV92] Since j F 2 3 2 the result then follows. In the perspective of such a relationship, future work includes the ....

J.A. Bergstra, J.W. Klop, and E.-R. Olderog. Readies and failures in the algebra of communicating processes. SIAM Journal on Computing, 17:1134--1177, 1988.

No context found.

J.A. Bergstra, J.W. Klop and E.R. Olderog. Readies and failures in the algebra of communicating processes. SIAM Journal of Computing, 17(6):11341177, 1988.

No context found.

J.A. Bergstra, J.W. Klop, and E.-R. Olderog. Readies and failures in the algebra of communicating processes. SIAM J. on Comput., 17:1134--1177, 1988.

No context found.

J.A. Bergstra, J.W. Klop, and E.-R. Olderog. Readies and failures in the algebra of communicating processes. SIAM J. on Comput., 17:1134--1177, 1988.

No context found.

J. A. Bergstra, J. W. Klop, and E.-R. Olderog. Readies and failures in the algebra of communicating processes. SIAM Journal of Computing, 17:1134--1177, 1988.

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