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Algebraic Process Verification
 Handbook of Process Algebra, chapter 17
"... 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. ..."
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Cited by 68 (16 self)
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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.
The safety guaranteeing system at station HoornKersenboogerd

"... At the Dutch station HoornKersenboogerd, computer equipment is used for the safe and in time movement of trains. The computer equipment can be divided in two layers. A top layer offering an interface and means to help a human operator in scheduling train movement. And a bottom layer which checks wh ..."
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Cited by 45 (4 self)
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At the Dutch station HoornKersenboogerd, computer equipment is used for the safe and in time movement of trains. The computer equipment can be divided in two layers. A top layer offering an interface and means to help a human operator in scheduling train movement. And a bottom layer which checks whether commands issued by the top layer can safely be executed by the rail hardware and which acts appropriately on detection of a hazardous situation. The bottom layer is implemented with a programmable piece of equipment namely a Vital Processor Interlocking (VPI). This paper introduces the most important features of the VPI at HoornKersenboogerd. This particular VPI is modelled in CRL. Furthermore, the paper touches upon correctness criteria and tool support for VPIs, and suggests ways for verification of properties of VPIs. Experiments show that it is indeed possible to efficiently verify these correctness criteria.
Focus points and convergent process operators: A proof strategy for protocol verification
, 1995
"... We present a strategy for finding algebraic correctness proofs for communication systems. It is described in the setting of µCRL [11], which is, roughly, ACP [2, 3] extended with a formal treatment of the interaction between data and processes. The strategy has already been applied successfully in [ ..."
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Cited by 41 (11 self)
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We present a strategy for finding algebraic correctness proofs for communication systems. It is described in the setting of µCRL [11], which is, roughly, ACP [2, 3] extended with a formal treatment of the interaction between data and processes. The strategy has already been applied successfully in [4] and [10], but was not explicitly identified as such. Moreover, the protocols that were verified in these papers were rather complex, so that the general picture was obscured by the amount of details. In this paper, the proof strategy is materialised in the form of definitions and theorems. These results reduce a large part of protocol verification to a number of trivial facts concerning data parameters occurring in implementation and specification. This greatly simplifies protocol verifications and makes our approach amenable to mechanical assistance � experiments in this direction seem promising. The strategy is illustrated by several small examples and one larger example, the Concurrent Alternating Bit Protocol (CABP). Although simple, this protocol contains a large amount of internal parallelism, so that all relevant issues make their appearance.
µCRL: A toolset for analysing algebraic specifications
 Proc. 13th Conference on Computer Aided Verification, LNCS 2102
, 2001
"... µCRL [13] is a language for specifying and verifying distributed systems in an algebraic fashion. It targets the specification of system behaviour in a processalgebraic style and of data elements in the form of abstract data types. The µCRL toolset [21] (see ..."
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Cited by 37 (18 self)
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µCRL [13] is a language for specifying and verifying distributed systems in an algebraic fashion. It targets the specification of system behaviour in a processalgebraic style and of data elements in the form of abstract data types. The µCRL toolset [21] (see
Verification of Temporal Properties of Processes in a Setting with Data
 In A.M. Haeberer, editor, AMAST’98, volume 1548 of LNCS
, 1999
"... . We define a valuebased 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 satisfacti ..."
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Cited by 26 (9 self)
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. We define a valuebased 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 firstorder 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...
A Bounded Retransmission Protocol for Large Data Packets. A Case Study in Computer Checked Algebraic Verification
"... This note describes a protocol for the transmission of data packets that are too large to be transferred in their entirety. Therefore, the protocol splits the data packets and broadcasts it in parts. It is assumed that in case of failure of transmission through data channels, only a limited number o ..."
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Cited by 20 (8 self)
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This note describes a protocol for the transmission of data packets that are too large to be transferred in their entirety. Therefore, the protocol splits the data packets and broadcasts it in parts. It is assumed that in case of failure of transmission through data channels, only a limited number of retries are allowed (bounded retransmission). If repeated failure occurs, the protocol stops trying and the sending and receiving protocol users are informed accordingly. The protocol and its external behaviour are speci ed in CRL. The correspondence between these is shown using the axioms of CRL. The whole proof of this correspondence has been computer checked using the proof checker Coq. This provides an example showing that proof checking of realistic protocols is feasible within the setting of process algebras.
Formalizing Process Algebraic Verifications in the Calculus of Constructions
"... This paper reports on the first steps towards the formal verification of correctness proofs of reallife protocols in process algebra. We show that proofs can be verified, and partly constructed, by a general purpose proof checker. The process algebra we use is µCRL, ACP augmented with data, wh ..."
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Cited by 18 (7 self)
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This paper reports on the first steps towards the formal verification of correctness proofs of reallife protocols in process algebra. We show that proofs can be verified, and partly constructed, by a general purpose proof checker. The process algebra we use is µCRL, ACP augmented with data, which is small enough to make the verification feasible, and at the same time expressive enough for the specification of reallife protocols. The proof checker we use is Coq, which is based on the Calculus of Constructions, an extension of simply typed lambda calculus. The focus is on the translation of the proof theory of µCRL and µCRLspecifications to Coq. As a case study, we verified the Alternating Bit Protocol.
Parameterised Boolean Equation Systems
 In Theoretical Computer Science
, 2004
"... Boolean equation system are a useful tool for verifying formulas from modal mucalculus 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 ..."
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Cited by 17 (8 self)
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Boolean equation system are a useful tool for verifying formulas from modal mucalculus 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 socalled parameterised boolean equation system, or equation system for short. In this article we focus on techniques to solve such equation systems.
The Parallel Composition of Uniform Processes with Data
 Theoretical Computer Science
, 2001
"... A general basis for the definition of a finite but unbounded number of parallel processes is the equation S(n; dt) = P (0; get(0; dt))/ eq(n; 0) .(P (n; get(n; dt)) k S(n \Gamma 1; dt)). In this formula eq(n; 0) is an equality test, and get(n; dt) denotes the nth data element in table dt . We deri ..."
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Cited by 13 (2 self)
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A general basis for the definition of a finite but unbounded number of parallel processes is the equation S(n; dt) = P (0; get(0; dt))/ eq(n; 0) .(P (n; get(n; dt)) k S(n \Gamma 1; dt)). In this formula eq(n; 0) is an equality test, and get(n; dt) denotes the nth data element in table dt . We derive a linear process equation with the same behaviour as S(n; dt ), and show that this equation is welldefined, provided one adopts the principle CLRSP from [4]. In order to demonstrate the strength of our result, we use it for the analysis of a standard example. We show that n + 1 concatenated buffers form a queue of capacity n + 1. 1 Introduction Distributed algorithms are often configured as an arbitrarily large but finite set of processors that run a similar program. Using the formalism CRL (micro Common Representation Language [9]) this can be described, using recursion and operators for parallelism. Several benchmark verifications in CRL and process algebra are therefore based on the...