Many process algebras are defined by structural operational semantics (SOS). Indeed, most such definitions are nicely structured and fit the GSOS format of [15]. We give a procedure for converting any GSOS language definition to a finite complete equational axiom system (possibly with one infinitary induction principle) which precisely characterizes strong bisimulation of processes.

In a similar way as 2-categories can be regarded as a special case of double categories, rewriting logic (in the unconditional case) can be embedded into the more general tile logic, where also side-effects and rewriting synchronization are considered. Since rewriting logic is the semantic basis of several language implementation efforts, it is useful to map tile logic back into rewriting logic in a conservative way, to obtain executable specifications of tile systems. We extend the results of earlier work by two of the authors, focusing on some interesting cases where the mathematical structures representing configurations (i.e., states) and effects (i.e., observable actions) are very similar, in the sense that they have in common some auxiliary structure (e.g., for tupling, projecting, etc.). In particular, we give in full detail the descriptions of two such cases where (net) process-like and usual term structures are employed. Corresponding to these two cases, we introduce two ca...

Abstract. Van Glabbeek (1990) presented the linear time/branching time spectrum of behavioral equivalences for finitely branching, concrete, sequential processes. He studied these semantics in the setting of the basic process algebra BCCSP, and tried to give finite complete axiomatizations for them. Obtaining such axiomatizations in concurrency theory often turns out to be difficult, even in the setting of simple languages like BCCSP. This has raised a host of open questions that have been the subject of intensive research in recent years. Most of these questions have been settled over BCCSP, either positively by giving a finite complete axiomatization, or negatively by proving that such an axiomatization does not exist. Still some open questions remain. This paper reports on these results, and on the state-of-the-art in axiomatizations for richer process algebras with constructs like sequential and parallel composition. 1

This paper studies nested simulation and nested trace semantics over the language BCCSP, a basic formalism to express finite process behaviour. It is shown that none of these semantics affords finite (in)equational axiomatizations over BCCSP. In particular, for each of the nested semantics studied in this paper, the collection of sound, closed (in)equations over a singleton action set is not finitely based.

Abstract. This paper studies the equational theory of bisimulation equivalence over the process algebra BCCSP extended with the priority operator of Baeten, Bergstra and Klop. It is proven that, in the presence of an infinite set of actions, bisimulation equivalence has no finite, sound, ground-complete equational axiomatization over that language. This negative result applies even if the syntax is extended with an arbitrary collection of auxiliary operators, and motivates the study of axiomatizations using conditional equations. In the presence of an infinite set of actions, it is shown that, in general, bisimulation equivalence has no finite, sound, ground-complete axiomatization consisting of conditional equations over BCCSP. Sufficient conditions on the priority structure over actions are identified that lead to a finite, ground-complete axiomatization of bisimulation equivalence using conditional equations. 1

2-nested simulation was introduced by Groote and Vaandrager [10] as the coarsest equivalence included in completed trace equivalence for which the tyft/tyxt format is a congruence format. In the linear time-branching time spectrum of van Glabbeek [8], 2-nested simulation is one of the few equivalences for which no finite equational axiomatization is presented. In this paper we prove that such an axiomatization does not exist for 2-nested simulation.

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We prove that testing preorder of De Nicola and Hennessy is preserved by all operators of De Simone process languages. Building upon this result we propose an algorithm for generating axiomatisations of testing preorder for arbitrary De Simone process languages. The axiom systems produced by our algorithm are finite and complete for processes with nite behaviour. In order to achieve completeness for a subclass of processes with infiite behaviour we use one infinitary induction rule. The usefulness of our results is illustrated in specification and verification of small concurrent systems, where suspension, resumption and alternation of execution of component systems occur. We argue that better speci cations can be written in customised De Simone process languages, which contain both the standard operators as well as new De Simone operators that are specifically tailored for the task in hand. Moreover, the automatically generated axiom systems for such specification languages make the verification more straightforward.

this paper has generated a veritable industry of results on the meta-theory of SOS and process algebras. (See [10] for a mention of some of these achievements and pointers to the original literature.) The proof techniques used in these results were extremely ingenious, and have paved the way to many similar developments. Again, the role played by the modal characterizations of behavioural equivalences in the proof of the characterizations of the largest congruences is remarkable

Abstract. We prove a unique decomposition theorem for a class of ordered commutative monoids. Then, we use our theorem to establish that every weakly normed process definable in ACP ε with bounded communication can be expressed as the parallel composition of a multiset of weakly normed parallel prime processes in exactly one way. 1