this paper have been presented at the 4th European Summer School in Logic, Language and Information, University of Essex, 1992; at the Tempus Summer School for Algebraic and Categorical Methods in Computer Science, Masaryk University, Brno, 1993; and the Summer School in Logic Methods in Concurrency, Aarhus University, 1993. I would like to thank the organisers and the participants of these summer schools, and of the Banff higher order workshop. I would also like to thank Julian Bradfield for use of his Tex tree constructor for building derivation trees and Carron Kirkwood, Faron Moller, Perdita Stevens and David Walker for comments on earlier drafts.

In model checking for temporal logic, the correctness of a (concurrent) system with respect to a desired behavior is verified by checking whether a structure that models the system satisfies a formula describing the behaviour. Most existing verification techniques, and in particular those defined for concurrent calculi like as CCS, are based on a representation of the concurrent system by means of a labelled transition system. In this approach to verification, state explosion is one of the most serious problems. In this paper we present a new temporal logic, the selective mu-calculus, with the property that only the actions occurring in a formula are relevant to check the formula itself. We prove that the selective mu-calculus is as powerful as the mu-calculus. We define the notion of ae-bisimulation between transition systems: given a set of actions ae, a transition system ae-bisimulates another one if they have the same behaviour with respect to the actions in ae. We prove that, if t...

We refine an abstract property-oriented specification in the µ-calculus to a specification in Maude. As an intermediate step, we use a structured specification in the µ-calculus blended with propositions on states appropriate for object-oriented specification. We use the loose approach in refinement and refine data types as well as behavior. Throughout, our example is the bounded buffer.

this paper we present a new temporal logic, the selective mu-calculus, and an equivalence between transition systems based on the formulae of this logic. This property preserving equivalence can be used to reduce the size of transition systems. The equivalence (called ae-

In recent years many techniques have been developed for automatically verifying concurrent systems and most of them are based on the representation of the concurrent system by means of a transition system. State explosion is one of the most serious problems of this approach: often the prohibitive number of states renders the verification inefficient and, in some cases, impossible. We propose a method for reducing the state space of the transition system corresponding to a CCS process that suites deadlock analysis. The reduced transition system is generated by means of a non-standard operational semantics containing a set of rules which are, in some sense, an abstraction, preserving deadlock freeness, of the inference rules of the standard semantics. Our method does not build the standard transition system, but directly generates an abstract system with a fewer number of states, so saving memory space. We characterize a class of processes whose abstract transition system is not exponential in the number of parallel components. Keywords: process algebras, transition systems, state explosion, structural operational semantics, deadlock. 1 This work has been partially funded by Progetto Coordinato CNR ANATRA 1 1

In recent years many techniques have been developed for automatically verifying concurrent systems and most of them are based on a representation of the concurrent system by means of a transition system. State explosion is one of the most serious problems of this approach: in fact often the prohibitive number of states renders the verification inefficient and, in some cases, impossible. We propose an approach to the reduction of the state space of the transition system corresponding to a CCS process, which takes into account the deadlock freeness property. The reduced transition system is generated by means of a non-standard operational semantics containing a set of rules which are, in some sense, an abstraction, preserving deadlock freeness, of the inference rules of the standard semantics.

In this paper we present a verification methodology, using an action-based logic, able to check properties for full CCS terms, allowing also verification on infinite state systems. Obviously, for some properties we are only able to give a semidecision procedure. The idea is to use (a sequence of) finite state transition systems which approximate the, possibly infinite state, transition system corresponding to a term. To this end we define a particular notion of approximation, which is stronger than simulation, suitable to define and prove liveness and safety properties of the process terms. 1 Introduction Many verification environments are presently available which can be used to automatically verify properties of reactive systems specified by means of process algebras, with respect to behavioural relations and logical properties. Most of these environments [7, 12, 13, 19] are based on the hypothesis that the system can be modelled as a finite state Labelled Transition Systems (LTS) a...

The present Thesis addresses the problem of specification and verification of communicating systems with value passing. We assume that such systems are described in the well-known Calculus of Communicating Systems, or rather, in its value passing version. As a specification language we propose an extension of the Modal ¯-Calculus, a poly-modal first-order logic with recursion. For this logic we develop a proof system for verifying judgements of the form b ` E : \Phi where E is a sequential CCS term and b is a Boolean assumption about the value variables occurring free in E and \Phi. Proofs conducted in this proof system follow the structure of the process term and the formula. This syntactic approach makes proofs easier to comprehend and machine assist. To avoid the introduction of global proof rules we adopt a technique of tagging fixpoint formulae with all relevant information needed for the discharge of reoccurring sequents. We provide such tagged formulae with a suitable semantics...

LOTOS is a formal specification language for concurrent and distributed systems. Basic LOTOS is the version of LOTOS without value-passing. A widely used approach to verification of temporal properties is model checking. Often, in this approach the formal specification is translated into a labeled transition systems on which formulae expressing properties are checked. A problem of this verification technique is state explosion: concurrent systems are often represented by automata with a prohibitive number of states. In this paper we show how, given a set ae of actions, it is possible to automatically obtain for a Basic LOTOS program a reduced transition system to which only the arcs labeled by actions in ae belong. The set ae of actions plays a fundamental role in conjunction with a temporal logic defined by the authors in a previous paper: selective mu-calculus. The reduced system with respect to ae preserves the truth value of all selective mu-calculus formulae with actions...

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