This chapter addresses the question how to verify distributed and communicating systems in an e#ective way from an explicit process algebraic standpoint. This means that all calculations are based on the axioms and principles of the process algebras.

µCRL [13] is a language for specifying and verifying distributed systems in an algebraic fashion. It targets the specification of system behaviour in a process-algebraic style and of data elements in the form of abstract data types. The µCRL toolset [21] (see

. We define a value-based modal -calculus, built from firstorder formulas, modalities, and fixed point operators parameterized by data variables, which allows to express temporal properties involving data. We interpret this logic over Crl terms defined by linear process equations. The satisfaction of a temporal formula by a Crl term is translated to the satisfaction of a first-order formula containing parameterized fixed point operators. We provide proof rules for these fixed point operators and show their applicability on various examples. 1 Introduction In recent years we have applied process algebra in numerous settings [4, 8, 12]. The first lesson we learned is that process algebra pur sang is not very handy, and we need an extension with data. This led to the language Crl (micro Common Representation Language) [13]. The next observation was that it is very convenient to eliminate the parallel operator from a process description and reduce it to a very restricted form, whi...

. In existing simulation proof techniques, a single step in a lowlevel system may be simulated by an extended execution fragment in a high-level system. As a result, it is undecidable whether a given relation is a simulation, even if tautology checking is decidable for the underlying specification logic. This paper introduces various types of normed simulations. In a normed simulation, each step in a low-level system can be simulated by at most one step in the high level system, for any related pair of states. We show that it is decidable whether a given relation is a normed simulation relation, given that tautology checking is decidable. We also prove that, at the semantic level, normed simulations form a complete proof method for establishing behavior inclusion, provided that the high-level system has finite invisible nondeterminism. As an illustration of our method we discuss the verification in PVS of a leader election algorithm that is used within the IEEE 1394 protocol. 1 Introdu...

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Abstract. We define a cones and foci proof method, which rephrases the question whether two system specifications are branching bisimilar in terms of proof obligations on relations between data objects. Compared to the original cones and foci method from Groote and Springintveld [22], our method is more generally applicable, and does not require a preprocessing step to eliminate τ-loops. We prove soundness of our approach and give an application. 1

In this note we present an algebraic verification of Segall's Propagation of Information with Feedback (PIF) algorithm. This algorithm serves as a nice benchmark for verification exercises (see [2, 13, 8]). The verification is based on the methodology presented in [7] and demonstrates its applicability to distributed algorithms.

Studying industrial systems by simulation enables the designer to study the dynamic behaviour and to determine some characteristics of the system. Unfortunately, simulation also has some disadvantages. These can be overcome by using formal methods. Formal methods allow a thorough analysis of the possible behaviours of a system, parameterised system analysis and a modular approach to the analysis of systems. We present a case study in which a model of an industrial system is studied in a formal way. For this purpose, the model is first specified and simulated using the CSP-based executable specification language Ø. The model is translated into a model in the process algebra ACP ø . This enables us to give a correctness proof of the parameterised model and to study the model in isolation. 1. Introduction Nowadays, industry makes higher demands on methodologies used for the design of new factories. Firstly, due to the huge amount of money involved and growing competition on the market...

We provide a treatise about checking proofs of distributed systems by computer using general purpose proof checkers. In particular, we present two approaches to verifying and checking the verification of the Sequential Line Interface Protocol (SLIP), one using rewriting techniques and one using the so-called cones and foci theorem. Both verifications are carried out in the setting of process algebra. Finally, we present an overview of literature containing checked proofs. Note: The research of the second author is supported by Human Capital Mobility (HCM). 1 Proof checkers Anyone trying to use a proof checker, e.g. Isabelle [67, 68], HOL [29], Coq [20], PVS [78], Boyer-Moore [14] or many others that exist today has experienced the same frustration. It is very difficult to prove even the simplest theorem. In the first place it is difficult to get acquainted to the logical language of the system. Most systems employ higher order logics that are extremely versatile and expressive. Howev...