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. We present a finite ω-complete axiomatization for the process algebra BCCSP modulo failure semantics, in case of a finite alphabet. This solves an open question by Groote [12]. 1

Abstract. We prove that if a finite alphabet of actions contains at least two elements, then the equational theory for the process algebra BCCSP modulo any semantics no coarser than readiness equivalence and no finer than possible worlds equivalence does not have a finite basis. This semantic range includes ready trace equivalence. 1

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

Abstract. This paper studies the (in)equational theory of simulation preorder and equivalence over the process algebra BCCSP. We prove that in the presence of a finite alphabet with at least two actions, the (in)equational theory of BCCSP modulo simulation preorder or equivalence does not have a finite basis. In contrast, in the presence of an alphabet that is infinite or a singleton, the equational theory for simulation equivalence does have a finite basis. 1

Abstract. We prove that the equational theory of the process algebra BCCSP modulo completed simulation equivalence does not have a finite basis. Furthermore, we prove that with a finite alphabet of actions, the equational theory of BCCSP modulo ready simulation equivalence does not have a finite basis. In contrast, with an infinite alphabet, the latter equational theory does have a finite basis. 1

Abstract. We give an axiomatisation of strong bisimilarity on a small fragment of CCS that does not feature the sum operator. This axiomatisation is then used to derive congruence of strong bisimilarity in the finite π-calculus in absence of sum. To our knowledge, this is the only nontrivial subcalculus of the π-calculus that includes the full output prefix and for which strong bisimilarity is a congruence.