This paper describes a procedure, based around the construction of tableau proofs, for determining whether finite-state systems enjoy properties formulated in the propositional mu-calculus. It presents a tableau-based proof system for the logic and proves it sound and complete, and it discusses techniques for the efficient construction of proofs that states enjoy properties expressed in the logic. The approach is the basis of an ongoing implementation of a model checker in the Concurrency Workbench, an automated tool for the analysis of concurrent systems. 1 Introduction One area of program verification that has proven amenable to automation involves the analysis of finite-state processes. While computer systems in general are not finite-state, many interesting ones, including a variety of communication protocols and hardware systems, are, and their finitary nature enables the development and implementation of decision procedures that test for various properties. Model checking has p...

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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.

Abstract. This paper presents a method for the decomposition of HML formulae. It can be used to decide whether a process algebra term satisfies a HML formula, by checking whether subterms satisfy certain formulae, obtained by decomposing the original formula. The method uses the structural operational semantics of the process algebra. The main contribution of this paper is that an earlier decomposition method from Larsen [14] for the De Simone format is extended to the more general ntyft/ntyxt format without lookahead. 1

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Machine CHAM [BB90]. CHAM has consequently been used to define one of the semantics of Facile [LT92b]. Also [NT92a] demonstrates the use of CHAM to define the semantics of a language that combines functional programming with concurrency, although in that work there is a parallel composition operator and not a fork operator. Section 3.1 defines the calculus with its operational semantics. Section 3.2 defines a strong congruence relation between processes. A congruence relation is an equivalence relation, which is preserved by the operators of the calculus. The congruence is strong since it is sensitive to internal transitions. Section 3.3 defines a weak congruence relation which is not sensitive to internal transitions. 3.1 Syntax and Semantics 3.1.1 Syntax and Informal Semantics The syntax, generating the language L, is as follows. p ::= nil j ff j p 1 + p 2 j p 1 ; p 2 j fork(p) j N 25 26 CHAPTER 3. THE FORK CALCULUS ff ::= j a? j a! The language A of actions is ranged over b...

The propositional µ-calculus of Kozen extends modal logic with fixed points to achieve a powerful logic for expressing temporal properties of systems modelled by labelled transition systems. We further extend Kozen's logic with polyadic modalities to allow for expressing also quite naturally behavioural relations like bisimulation equivalence and simulation preorders. We show that the problem of model checking is still efficiently decidable, giving rise to efficient worst-case algorithms for verifying the infinity of behavioural relations expressible in this polyadic modal µ-calculus. Some of these algorithms compete in efficiency with carefully hand-crafted algorithms found in the literature. In spite of this result, the validity problem turns out to be highly undecidable. This is in contrast to the propositional µ-calculus where it is decidable in deterministic exponential time. It follows as a corollary, that -- also in contrast to the propositional µ-calculus -- the polyadic modal...