I. Ulidowski. Axiomatisations of weak equivalences for De Simone languages. In I. Lee and S.A. Smolka, editors, Proceedings of the 6th International Conference on Concurrency Theory CONCUR'95, Philadelphia, 1995. Springer. LNCS 962.  Home/Search   Document Details and Download   Summary   Related Articles   Check

....that match: the axiomatization should be sound and complete for the model of transition systems modulo (strong) bisimulation. The paper [ABV94] points the way in such an endeavour: in some cases an axiomatization can be derived by just following a recipe. Some other papers in this area are [Uli95, Uli00] (where other equivalence relations besides bisimulation equivalence are considered) However, in the years since the appearance of these papers, we have seen no application of the theory. The reader may wonder why this is so. In our opinion, this is due to the limited process algebraic basis ....

I. Ulidowski. Axiomatisations of weak equivalences for De Simone languages. In I. Lee and S. Smolka, editors, Proc. CONCUR'95, pages 219-233. LNCS 962, 1995.

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I. Ulidowski. Axiomatisations of weak equivalences for De Simone languages. In I. Lee and S.A. Smolka, editors, Proceedings of the 6th International Conference on Concurrency Theory CONCUR'95, Philadelphia, 1995. Springer. LNCS 962.

....a number of improvements to our procedure and outlines future work. Due to the lack of space the proofs of our results are not included in this paper. These proofs as well as examples illustrating the applications of our axiomatisation procedure can be found in the full version of the paper [Uli95]. 2 Preliminaries This section defines notions of DeS process languages, labelled transition systems with divergence and refusal simulation preorder. We assume a knowledge of basic ideas, definitions and results for process algebras as, for example, in [BHR84, Mil89, Hen88, BW90, BIM88, GV90] ....

.... p v q; p = q) to mean that p v q; p = q) can be derived from the axiomatic theory T. Theorem 8. RS p v q if and only if RSim(B) ffl p v q. The completeness part is proved, as usual, by extracting normal and head normal forms. Their definitions and the details of the proof can be found in [Uli95]. 4 Deriving Sound Axioms for DeS Process Languages In this section, we give a procedure for deriving sound axiomatisations of refusal simulation preorder for arbitrary DeS process languages. The derived axiomatisations are head normalising, but they are infinite and conditional. We ....

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I. Ulidowski. Axiomatisations of weak equivalences for De Simone languages. Technical report, RIMS, Kyoto University, 1995.

.... example, a number of important preorders and equivalences on processes were shown to be congruences for certain classes of process languages [BIM88, BIM95, GV90, Gro90, Vaa91, Uli92, Blo95a, Uli94] Axiomatic systems and denotational models for these classes of process languages were proposed in [ABV92, ABV94, Ace94, Uli95] and [AI95] respectively. Also, two classes of languages were used in [Blo95b] as general specification languages. This paper continues the research related to general process languages. We consider a class of process languages generated by the De Simone format of rules with a special treatment of ....

....used in [Blo95b] as general specification languages. This paper continues the research related to general process languages. We consider a class of process languages generated by the De Simone format of rules with a special treatment of silent actions. This class, denoted by DeS, was defined in [Uli95]. Out of many preorders (equivalences) proposed in the concurrency literature we consider testing preorder of De Nicola and Hennessy [NH84, Nic87, Hen88] which is based on an intuitive notion of comparing responses of processes to tests. The first contribution of this paper is the proof that ....

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I. Ulidowski. Axiomatisations of weak equivalences for De Simone languages. In I. Lee and S.A. Smolka, editors, Proceedings of the 6th International Conference on Concurrency Theory CONCUR'95, Philadelphia, 1995. Springer-Verlag. LNCS 962.

.... weak equivalences were shown to be preserved by all process operators in these formats [10, 9, 12] Secondly, completed) trace congruences with respect to these formats were discovered [10, 11] Thirdly, algorithms for generating complete axiomatisations of some weak equivalences were developed [13, 14, 15]. The main conceptual contribution of the paper is a new method for defining process operators, including the sequential composition and priority operators, by transition rules with no negative antecedents. Our method is based on a simple idea of ordering the transition rules for each operator. ....

I. Ulidowski. Axiomatisations of weak equivalences for De Simone languages. In I. Lee and S.A. Smolka, editors, Proceedings of the 6th International Conference on Concurrency Theory CONCUR'95, Philadelphia, 1995. Springer-Verlag. LNCS 962.

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