Least fixpoints as meanings of recursive definitions.

Model-checking is a successful technique for automatically verifying concurrent finite-state systems. When building a model-checker, a good compromise must be made between the expressive power of the property description formalism, the complexity of the model-checking problem, and the user-friendliness of the interface. We present a temporal logic and an associated model-checking method that attempt to fulfill these criteria. The logic is an extension of the alternation-free µ-calculus with ACTL-like action formulas and PDL-like regular expressions, allowing a concise and intuitive description of safety, liveness, and fairness properties over labeled transition systems. The model-checking method is based upon a succinct translation of the verification problem into a boolean equation system, which is solved by means of an efficient local algorithm having a good average complexity. The algorithm also allows to generate full diagnostic information (examples and counterexamples) for temporal for...

We briefly survey the background and history of modal and temporal logics. We then concentrate on the modal mu-calculus, a modal logic which subsumes most other commonly used logics. We provide an informal introduction, followed by a summary of the main theoretical issues. We then look at model-checking, and finally at the relationship of modal logics to other formalisms.

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We present a new block diagram language for describing synchronous software. It coordinates the execution of synchronous, concurrent software modules, allowing real-time systems to be assembled from precompiled blocks specified in other languages. The semantics we present, based on fixed points, is deterministic even in the presence of instantaneous feedback. The execution policy develops a static schedule—a fixed order in which to execute the blocks that makes the system execution predictable. We present exact and heuristic algorithms for finding schedules that minimize system execution time, and show that good schedules can be found quickly. The scheduling algorithms are applicable to other problems where large systems of equations need to be solved.

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) Henrik Reif Andersen Department of Computer Science Technical University of Denmark Building 344, DK-2800 Lyngby, Denmark. Abstract A major obstacle in applying finite-state model checking to the verification of large systems is the combinatorial explosion of the state space arising when many loosely coupled parallel processes are considered. The problem also known as the state-explosion problem has been attacked from various sides. This paper presents a new approach based on partial model checking: Parts of the concurrent system are gradually removed while transforming the specification accordingly. When the intermediate specifications constructed in this manner can be kept small, the stateexplosion problem is avoided. Experimental results with a prototype implemented in Standard ML, shows that for Milner's Scheduler --- an often used benchmark --- this approach improves on the published results on Binary Decision Diagrams and is comparable to results obtained using generalized...

We present a proof system for determining satisfaction between processes in a fairly general process algebra and assertions of the modal µ-calculus. The proof system is compositional in the structure of processes. It extends earlier work on compositional reasoning within the modal µ-calculus and combines it with techniques from work on local model checking. The proof system is sound for all processes and complete for a class of finite-state processes.

Boolean equation system are a useful tool for verifying formulas from modal mu-calculus on transition systems (see [18] for an excellent treatment). We are interested in an extension of boolean equation systems with data. This allows to formulate and prove a substantially wider range of properties on much larger and even infinite state systems. In previous works [11, 15] it has been outlined how to transform a modal formula and a process, both containing data, to a so-called parameterised boolean equation system, or equation system for short. In this article we focus on techniques to solve such equation systems.

We present a new algorithm for detecting semantic combinational cycles that is simpler and more efficient than earlier algorithms found in the literature. Combinational circuits with syntactic cycles often arise in processor and bus-based designs. The intention is that external inputs and delay elements such as latches break these cycles, so that no "semantic" cycles remain. Unbroken semantic cycles are considered a design error in this context. Such unbroken cycles may also occur inadvertently in compositions of Mealy machines.