Formal methods and testing are two important approaches that assist in the development of high quality software. While traditionally these approaches have been seen as rivals, in recent years a new consensus has developed in which they are seen as complementary. This article reviews the state of the art regarding ways in which the presence of a formal specification can be used to assist testing.

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This paper provides new insight into the connection between the trace-based lower part of van Glabbeek's linear-time, branching-time spectrum and its simulation-based upper part. We establish that ready simulation is fully abstract with respect to failures inclusion, when adding the conjunction operator that was proposed by the authors in [TCS 373(1-2):19-40] to the standard setting of labelled transition systems with (CSP-style) parallel composition. More precisely, we actually prove a stronger result by considering a coarser relation than failures inclusion, namely a preorder that relates processes with respect to inconsistencies that may arise under conjunctive composition. Ready simulation is also shown to satisfy standard logic properties and thus commends itself for studying mixed operational and logic languages.

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We present a method for the compositional construction of the minimal transition system that represents the semantics of a given distributed system. Our aim is to control the state explosion caused by the interleavings of actions of communicating parallel components by reduction steps that exploit global communication constraints given in terms of interface specifications. The effect of the method, which is developed for bisimulation semantics here, depends on the structure of the distributed system under consideration, and the accuracy of the interface specifications. However, its correctness is independent of the correctness of the interface specifications provided by the program designer.

A key problem in mixing operational (e.g. process-algebraic) and declarative (e.g. logical) styles of specification is how to deal with inconsistencies arising when composing processes under conjunction. This article introduces a conjunction operator on labelled transition systems capturing the basic intuition of 'a and b = false', and considers a naive preorder that demands that an inconsistent specification can only be refined by an inconsistent implementation.The main body of the article is concerned with characterizing the largest precongruence contained in the naive preorder. This characterization will be based on what we call ready-tree semantics, which is a variant of path-based possible-worlds semantics. We prove that the induced ready-tree preorder is compositional and fully abstract, and that the conjunction operator indeed reflects conjunction.The article's results provide a foundation for, and an important step towards a unified framework that allows one to freely mix operators from process algebras and linear-time temporal logics.

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Abstract. More than a decade ago, Moller and Tofts published their seminal work on relating processes that are annotated with lower time bounds, with respect to speed. Their paper has left open many questions concerning the semantic theory for their suggested bisimulation-based faster-than preorder, the MT-preorder, which have not been addressed since. The encountered difficulties concern a general compositionality result, a complete axiom system for finite processes, and a convincing intuitive justification of the MT-preorder. This paper solves these difficulties by developing and employing novel tools for reasoning in discrete-time process algebra, in particular a general commutation lemma relating the sequencing of action and clock transitions. Most importantly, it is proved that the MT-preorder is fullyabstract with respect to a natural amortized preorder that uses a simple bookkeeping mechanism for deciding whether one process is faster than another. Together these results reveal the intuitive roots of the MTpreorder as a faster-than relation, while testifying to its semantic elegance. This lifts some of the barriers that have so far hampered progress in semantic theories for comparing the speed of processes.