Abstract The Concurrency Workbench is an automated tool for analyzing networks of finite-state processes expressed in Milner's Calculus of Communicating Systems. Its key feature is its breadth: a variety of different verification methods, including equivalence checking, preorder checking, and model checking, are supported for several different process semantics. One experience from our work is that a large number of interesting verification methods can be formulated as combinations of a small number of primitive algorithms. The Workbench has been applied to the verification of communications protocols and mutual exclusion algorithms and has proven a valuable aid in teaching and research. 1 Introduction This paper describes the Concurrency Workbench [11, 12, 13], a tool that supports the automatic verification of finite-state processes. Such tools are practically motivated: the development of complex distributed computer systems requires sophisticated verification techniques to guarantee correctness, and the increase in detail rapidly becomes unmanageable without computer assistance. Finite-state systems, such as communications protocols and hardware, are particularly suitable for automated analysis because their finitary nature ensures the existence of decision procedures for a wide range of system properties.

In this paper we develop a compositional method for the construction of the minimal transition system that represents the semantics of a given reactive system. The point of this method is that it exploits structural properties of the reactive system in order to avoid the consideration of large intermediate representations. Central is the use of interface specifications here, which express constraints on the components' communication behaviour, and therefore to control the state explosion caused by the interleavings of actions of communicating parallel components. The effect of the method, which is developed for bisimulation semantics here, depends on the structure of the reactive system under consideration, in particular on the accuracy of the interface specifications. However, its correctness does not: every "successful" construction is guaranteed to yield the desired minimal transition system, independently of the correctness of the interface specifications provided by the designer.

This paper develops a model-checking algorithm for a fragment of the modal mu-calculus and shows how it may be applied to the efficient computation of behavioral relations between processes. The algorithm's complexity is proportional to the product of the size of the process and the size of the formula, and thus improves on the best existing algorithm for such a fixed point logic. The method for computing preorders that the model checker induces is also more efficient than known algorithms.

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