J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77--121, 1985.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....on shared variables, synchronous systems, reactive systems, timed systems, mobile systems or secure systems. There are many models for concurrent systems. Some examples of synchronous models are the process calculi of Milner s CCS [Mil89] Hoare s CSP [Hoa85] or the ACP of Bergstra and Klop [BK85] The model which we consider in this thesis is the model for concurrency that was de ned in [Sar89] The Concurrent Constraint programming paradigm (cc) was de ned by Saraswat and Rinard in [Sar89, Sar93, SR90] as a simple and powerful model of concurrent computation. In such computational ....

J.A. Bergstra and J. W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37:77-121, 1985.

....etc. However, there are also some classes that not in C. For example, Basic Parallel Processes [Chr93] are not in C, because they are not closed under synchronization (condition 3) Pushdown automata are not in C, because they are not closed under parallel composition (condition 2) PA processes [BK85] are not in C, because they are not closed under synchronization and because their transition rules are not injective (they do not satisfy conditions 1 and 3) # is (isomorphic to) A comp(T M 1 TM 2 ) Proof. Follows immediately from condition 1 (which enables efficient renaming of ....

J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37:77--121, 1985.

....transition relation is the union of the untimed transition relations of the combined timed transitions. The resulting time step relation is the intersection of the time step relations of the combined timed transitions. We introduce standard process algebra notation to represent timed systems [BK85] A discrete labeled transition system (S; A) can be represented as a set of equations of the form s = i2I a i :s i where f(s; a i ; s i )g i2I is the set of all the transitions issued from s 2 S and the right hand sides of the equations are terms p of the form, p : N il j s 2 S j a:p j p ....

J. A. Bergstra and J. W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77--121, May 1985. Fundamental studies.

.... transitions but may differ in urgency (ability to perform actions within a given delay) We assume that parallel composition of two discrete systems can be expressed as the non deterministic choice of terms starting with interleaving or synchronization actions (by means of some expansion theorem [BK85] The expansion theorem is extended to hybrid actions in the following manner : To guarantee maximal progress, non deterministic choice is replaced by priority choice that gives higher priority to synchronization actions over interleaving actions. Synchronization operators between ....

....composition of untimed terms. For this, we suppose that the vocabulary of actions A contains a distinguished element and consider the set A p of the words generated from A with a commutative operator such that for all a, a p = The operator is usually called communication function [BK85] The words are used to represent synchronization actions that is, actions that result from the synchronous occurrence of atomic actions. a 1 a 2 = means impossibility of synchronization. In the sequel, we suppose that there are no other simplification rules for but the rule for and ....

J. A. Bergstra and J. W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77--121, May 1985. Fundamental studies.

....very simple, operators, including: 1. atomic actions, often regarded as communication along channels; 2. parallel composition; 3. sequencing; 4. non deterministic choice. All these features are present in process algebras like ACP, the Algebra of Communicating Processes of Bergstra an Klop [BK85, BW90] CSP, the Communicating Sequential Processes of Hoare [Hoa85] and CCS, the Calculus of Communicating Systems of Milner [Mil89a] Data structures are easily de ned using the basic constructors, and values of the data structures can be send along the communication channels. In all, the ....

....completeness. The study of image in nite (or in nitestate) systems is a lively area of concurrency theory, with several important results established [BE97, CH93, Mol96] We focus our attention in two process algebras: BPA and BPP. BPA is the class of Basic Process Algebra of Bergstra and Klop [BK85] corresponding to the transition systems associated with Greibach Normal Form (GNF) context free grammars, in which only left most derivations are allowed. BPP is the class of Basic Parallel Processes of Christensen [Chr93] which is the parallel counterpart of BPA but with arbitrary ....

Jan A. Bergstra and Jan W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77-121, 1985.

....event based. Examples of state based approaches include those of Z [Spi92] Object Z [DRS95] B [Abr96] and the Vienna Development Method (VDM) Jon90] Examples of event based approaches include those of Communicating Sequential Processes (CSP) Hoa85] Algebra for Communicating Processes (ACP) BK85] and Calculus for Communicating Systems (CCS) Mil80, Mil89] The information contained within models describing the same system in state based and event based approaches might be the same, but the means of reasoning is di#erent. Each method has its own tools and techniques for analysing models. ....

....or axioms, that capture the properties of the operators: whether they are symmetric, associative, commutative, or idempotent; whether one operator distributes over another. Process equivalence can then be derived from these laws. An example of a process algebra that takes this approach is ACP [BK85] A denotational semantic model describes processes in a di#erent fashion. The model is defined by a function that maps the language onto a mathematical description of its behaviour. A denotational semantic model is normally a congruence: given a semantic that defines the model, any (binary) ....

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J. A. Bergstra and J. W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1), 1985.

....of concurrent systems, and includes formalisms for modelling, expressing properties, validation and verification of such systems. The history of the theory of concurrency started more than thirty years ago. Various models of communicating systems, such as Petri nets [44] CSP [13] ACP [2], CCS [24, 25] the # calculus ( 27] have been proposed since then. Robin Milner s invention of the Calculus of Communicating Systems (CCS) was a cornerstone in the history of theory of concurrency. CCS deals with interactive systems which are not mobile and was designed to help understanding ....

J.A. Bergstra and J-W. Klop. Algebra of communicating processes with abstractions. Theoretical Computer Science, 33:77--121, 1985.

....been focused on process algebras and the modal calculus. The characteristic feature of process algebras is the use of an algebraic syntax which provides operators to build larger processes from smaller ones. Several algebraic process calculi have been considered, such as CSP [22] CCS [29] or ACP [26], their main objective is to allow the modelling of concurrent system in an abstract formal framework. The modal calculus is a very powerful temporal logic which combines standard modal logic with least and greatest fixed point operators. It is of particular interest since it subsumes many other ....

....in concurrency theory is to describe processes as terms in a process algebra. Several algebraic frameworks have been considered in this aim, such as the Calculus of Communicating Systems (CCS) introduced by Milner [29] or the Algebra of Communicating Processes (ACP) due to Bergstra and Klop [26]. Both systems allow the specification of very powerful computational systems, which has the drawback that many interesting problems are infeasible. Consequently, several sub calculi have been considered. In this report, we will consider the Basic Process Algebra (BPA) 26] a subclass of ACP. ....

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J.A. Bergstra and J.W. Klop. Algebra of Communicating Processes with Abstraction. Theoretical Computer Science, 37(1):77--121, 1985.

....transparent, because replication is obtained without changingproducer or consumer. This solution has been validated in CRL and its correctness has been proved in general using PVS. 3. THE CRL APPROACH The CRL [15] specification language is a combination of (ACP style) process algebra (see e.g. [1, 12]) and algebraic datatypes. A system is modeled as a process , often specified as the parallel composition ( ofanumberof other processes, the components. Components are often described by recursive equations, using sequential ( andalternative ( composition. Consider, e.g. Buf = in.out.Buf ....

J. Bergstra and J. Klop. Algebra of communicating processes with abstraction. TCS, 37(1):77--121, 1985.

....into two categories: either the validity is modelled by an appropriate equivalence, or it is modelled by a non necessarily symmetric relation such as a preorder. Validity as an equivalence Equivalence relations play a central role in process algebraic languages such as CCS [Mil 89] ACP [BeK 85] or LOTOS [ISO 8807, BoB 87] for reasoning about systems and analysing their properties. Many different notions of equivalence have been proposed, and this is not surprising since there are many properties which may be relevant in the analysis of distributed systems [dNi 87] However, these ....

J.A. Bergstra, J. W. Klop, Algebra of Communicating Processes with Abstraction, Theoretical Computer Science 37 (1985) 77-121 (North-Holland, Amsterdam).

....completeness. The study of image infinite (or infinitestate) systems is a lively area of concurrency theory, with several important results established [BE97, CH93, Mol96] We focus our attention in two process algebras: BPA and BPP. BPA is the class of Basic Process Algebra of Bergstra and Klop [BK85], corresponding to the transition systems associated with Greibach Normal Form (GNF) context free grammars, in which only left most derivations are allowed. BPP is the class of Basic Parallel Processes of Christensen [Chr93] which is the parallel counterpart of BPA but with arbitrary derivations. ....

Jan A. Bergstra and Jan W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77--121, 1985. 40

....34 left merge communication merge x x a A x ) x y y XIIAY X IIAY XIIAY X HAY x . x y . y a E A x x y ) y x IA Y x IIA Y x Y x Y left sequential right sequential residue x x aE [A]i SA( 4 Table 5: Operational semantics of auxiliary operators of ACP [10] for instance contains a rule for the right distributivity of sequential composition over choice: x 4. y)z = xz 4. yz (where juxtaposition is sequential composition) For weak sequential composition, however, this is not valid: for instance, if a I c I b, then (a 4. b) c (a 4. b) 1 which can ....

....c . However B whereas C , hence B C. What we need is some finer method, which also takes choices into account. For this, we introduce a further auxiliary operator, called deadlock (also defined in Table 5) The deadlock operator serves a purpose similar to the encapsulation operator of ACP [10]; however, the use of the index set is different. In general, 5A transforms a term B into a deadlocked term (i.e. 5A(B) for all a 6 Act) with the same termination behaviour as B, except that A is added to the alphabet. The following proposition (proof omitted) formalises this property: ....

J. A. Bergstra and J. W. Klop. Algebra of communicating processes with abstraction. Theoretical Cornput. Sci., 37(1):77-121, 1985.

....the initial semantics of the extended specification Speco, then any conservative extension of Speco preserves the no junk and no confusion properties of the initial semantics of Speco. 2. 2 Equational process algebra specification The behavior of a system wil be specified in process algebra [4, 5, 6, 7]. It is not customary to give a purely equational specification of this, so we give one in this subsection. New elements in this specification are the inclusion of an underlying ADT specification, the presence of actors, and an axiomatization of action negation. First, we define the relation ....

J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37:77-121, 1985.

....models. The missing features were the ability to specify object identifiers, local object states, and object dynamics. These were added in the rest of the paper, by defining a language called CMSL that extends the order sorted equational specification paradigm. Elsewhere [46] process algebra [7, 11] is added as well in order to define object life cycles. Normarive constraints [40, 47, 51] and actors [39, 41, 48] can be defined in CMSL as well. As promised in the introduction, oid s play a central role in CMSL, among others to localize object states and state changes. Current work on CMSL ....

J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37:77 121, 1985.

....later years in the wake of the study of processes. Seemingly independently, theories of processes were developed around the idea of communicating agents, performing atomic, indivisible, actions, 7, 50, 70] the calculi presented in [6, 74, 51] are the fruits of extensive research into processes, [10, 15, 44, 69, 71, 80] for example. These calculi all provide syntactic descriptions of communicating agents and, in the so called pure forms of these languages, communication is modelled solely by synchronisation so that the fact that actual data may be transmitted from one agent to another is abstracted away. This is ....

J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77--121, 1985. (p 1)

....their equivalences mechanically. Keyword Codes: D.3.1; F.4.3; F.3.2 Keywords: Timed LOTOS, Formal Definitions and Theory; First Order Logic, Mathematical Logic; Equivalence, Semantics of Program Languages 1. Introduction Formal languages based on Process Algebra, such as CCS[1] CSP[2] ACP[3], LOTOS[4] and so on, have been proposed to specify communication protocols and distributed systems. Although these languages can express temporal ordering of the actions, they cannot express explicit time constraints among the actions. It is necessary for the real time systems and communication ....

J.A. Bergstra and J. W. Klop, "Algebra of communicating processes with abstraction," Theoret. Cornput. Sci., vol. 37, pp. 77-121, 1985.

....# Q and P # Q and view # and # also as relations between processes. 512 Markus Muller Olm A AB a a a a c c c c . 2 3 B B B . e b b b b AB 2 AB 3 Fig. 1. A context free process Context Free Processes. Context free processes, also called BPA (basic process algebra) processes [1], are a certain type of finitely generated infinite state processes. Their name derives from the fact that they are induced by leftmost derivations of context free grammars in Greibach normal form, where the terminal symbols are interpreted as actions and the non terminals induce the state. ....

J. A. Bergstra and J. W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37:77--121, 1985.

....a semantic space. It is hence not surprising that most modern semantic models allow miracles (e.g. 10, 15, 17] For example, Nelson dropped the restriction in his generalisation of Dijkstra s calculus [17] GCL does not allow reactive behaviours. Reactiveness widely appears in computer science [2, 5, 6, 14, 15, 18, 19]. Reactive process are very di erent from sequential programs. Dunne [10] applied Nelson s Egli Milner order of GCL [17] to reactive computing and showed that the Egli Milner order is perhaps an order more natural for reactiveness than the re nement order. A model allowing in nite reactive ....

....Egli Milner order of GCL [17] to reactive computing and showed that the Egli Milner order is perhaps an order more natural for reactiveness than the re nement order. A model allowing in nite reactive behaviours (e.g. 5, 6, 18, 19] is much trickier than a model without in nite behaviours (e.g. [2, 14, 15, 19]) If we intend to reason about safety and liveness properties, the modelling of in nite reactive behaviours is inevitable. Another challenge is involved with the loops whose bodies are skip or any other command that does not generate intermediate states. For simplicity, ACP [2] does not allow ....

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J. A. Bergstra and J. W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77-121, 1985.

....BNNI ## E ActH #B (E I ActH ) Act H (ii) E # BSNNI ## E ActH #B E ActH As expected, it can be proved that each of these new properties is properly finer than its corresponding trace based one. Proposition 4. The following hold: i) BNNI # NNI, ii) BSNNI # SNNI, 8 BPA [6] are basically the transition systems associated with Greibach normal form (GNF) context free grammars in which only left most derivations are permitted. In order to obtain an lts an action is associated with every rule. E E P Low level User Fig. 8. BNDC intuition Proof. It immediately ....

J. A. Bergstra and J. W. Klop. "Algebra of Communicating Processes with Abstraction ". Theoretical Computer Science, 37:77--121, 1985.

....replication is obtained rather easily, without changing producer or consumer. This solution has been validated in CRL and its correctness has been proved in general using PVS. III. The CRL approach The CRL [15] speci cation language is a combination of (ACP style) process algebra (see e.g. [1], 12] and algebraic datatypes. A system is modeled as a process , often speci ed as the parallel composition (jj) of a number of other processes, the components. Components are often described by recursive equations, using sequential ( and alternative ( composition. Consider, e.g. Buf = ....

J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77-121, 1985.

....adding the axiom scheme (3.8) to an axiom system makes the axiom system infinite; yet, it might make it complete too. Many researchers have attempted to replace (3. 8) by a finite collection of equational axioms, in the context of CCS [Moller 89] and other process algebras [Bergstra Klop 84, Bergstra Klop 85, Hennessy 87, Castellani Hennessy 89] For CCS, however, it is a result that any sound and complete axiomatisation for any process equivalence, which is at least as strong as , is of necessity infinite [Moller 89] This explains why the expansion law is taken apart from any system ....

....algebraically, that linking two copies of a 1 bit buffer results in a 2 bit buffer. 1 [Sanderson 82] has found that it is possible to weaken the sequentiality condition and still guarantee uniqueness; moreover, Kranakis 86] has shown this still holds for sets of parameterised equations in ACP [Bergstra Klop 85] a process algebra very similar to CCS. CHAPTER 3. THE EQUATIONAL APPROACH TO VERIFICATION 36 A Worked Example Suppose that we wish to prove that C C = Buf h2;0i (3.12) Proof By using (3.10) and the expansion law respectively, we find that Buf h2;0i and C C satisfy the following systems of ....

J. A. Bergstra and J. W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77--121, 1985.

.... j i X B XB BB XBB oe oe oe a a a b b b c c c Delta Delta Delta Delta Delta Delta (When drawing automata, we shall indicate start states by short arrows and final states by double circles. Such grammars make up Bergstra and Klop s Basic Process Algebra (BPA) [4] and their associated automata are referred to as BPA processes. They are also instances of Caucal s Rewrite Transition Systems [8] We may also interpret concatenation of variables as parallel rather than sequential composition, by reading sequences of variables modulo commutativity of ....

.... ae ae ae ae= Z Z Z Z Z Z Z Z ae ae ae ae= a b c a a b c These two automata both recognise the same (regular) language f ab; ac g. However, they are substantially different automata. 4 As indicated above, BPA represents the class of Basic Process Algebra processes of Bergstra and Klop [4], which are the transition systems associated with GNF context free grammars in which only left most derivations are permitted. Example 2.4 In the following we present a type 2 (GNF context free grammar) rewrite system along with the BPA transition system which the initial state X denotes. X a ....

J.A. Bergstra and J.W. Klop (1985). Algebra of Communicating Processes with Abstraction. Theoretical Computer Science 37:77--121.

....such as temporal logics, assertional methods, net based models, automata theory and process algebras. In this paper, we provide an overview of the family of resource bound real time process algebras that we have developed. Process algebras, such as CCS [12] CSP [7] Acceptance Trees [5] and ACP [2], have been developed to describe and analyze communicating, concurrently executing systems. They are based on the premises that the two most essential notions in understanding complex dynamic systems are concurrency and communication [12] The most salient aspect of process algebras is that they ....

J.A. Bergstra and J.W. Klop. Algebra of Communicating Processes with Abstraction. Journal of Theoretical Computer Science, 37:77--121, 1985.

....the relation a : in any composition of elementary processes, only the first may make a transition, the second becoming active only when the first is exhausted. The context free processes that have been described form a fragment of the process algebra ACP (the Algebra of Communicating Processes) [2], known as BPA (Basic Process Algebra) This is just one of a number of algebraic formalisms, including, for example, Milner s CCS [16] and Hoare s CSP [10] that have been developed for specifying and reasoning about concurrent systems. As an example, consider the grammar given by the GNF rules ....

J.A. Bergstra and J.W. Klop. Algebra of Communicating Processes with Abstraction. Journal of Theoretical Computer Science 37(1) (1985), pp. 77--121.

....A a Gamma C B b Gamma C c Gamma A B C = a a b c These two automata both recognise the same (regular) language f ab; ac g. However, they are substantially different automata. BPA represents the class of Basic Process Algebra processes of Bergstra and Klop [9], which are the transition systems associated with Greibach normal form (GNF) context free grammars in which only left most derivations are permitted. 10 Example 1 In the following we present a type 2 (GNF context free grammar) rewrite system along with the BPA transition system ....

....various decidability and algorithmic results pertaining to other classes of processes which have been intensively studied. These are either extensions or restrictions of classes within our hierarchy, and are summarised below. PA Historically, the class BPA was first defined as a process algebra [9] with prefixing, nondeterministic choice, sequential composition, and recursion. Similarly, the class BPP was introduced by Christensen [35] as the parallel analogue to BPA, where sequential composition is replaced by parallel composition without communication. A natural extension of both classes ....

J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37:77--121, 1985.

....operators or combinators as possible, each of which embodies some distinct and intuitive idea, and which together give completely general expressive power. The addition of a single recursive operation to the process algebraic framework ACP (Algebra of Communicating Processes) with abstraction ( BK85, BW90] provides general expressive power: each computable process can be expressed. We consider two candidates for such a recursive operation. The distinct and intuitive idea embodied by each of these is a simple way of counting. Rather than focusing on a particular machine model for ....

J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77--121, 1985.

....C(Kn 2x)yz : So Kn 1 (Cxy) C(Kn 2x)y. We now have that Kn 1 ( Sigma x)y = Kn ( Sigma xy) Kn ( Sigma (Cxy) Sigma (Kn 1 (Cxy) by IH = Sigma (C(Kn 2x)y) Sigma (Kn 2x)y : Hence Kn 1 ( Sigma x) Sigma (Kn 2x) ut The second group of axioms consists of the ACP axioms introduced in [BK85] and extending the ACP axioms of [BK84] The schemata, from which the axioms can be obtained by a type assignment to the variables and operators, are listed in Table 5 and 6. They differ from all the other schemata in so far as only restricted type assignment is permitted. That is, the labels of ....

....= c 2 E ; x j rz 1 Delta Delta Delta z n and y j sz 1 Delta Delta Delta z n ffi A otherwise : We start building our model by fixing some family of nonempty sets (B ff ) ff2B with 1. BP is a model for ACP (T (B; F)A ; fl) e.g. a model in weak (or rooted ) bisimulation semantics (cf.[BK85], BBP93] and 2. B ff B fi iff ff fi. The family (B ff ) ff2B is intended to interpret the set of basic types B under preservation of its subtype relation. So, in the minimal case, B ff ) ff2B consists solely of the ACP model BP with subtypes BA and BA c , and a set BD . We now ....

J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77--121, 1985.

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J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77--121, 1985.

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J.A. Bergstra and J.W. Klop. Algebra of Communicating Processes with Abstraction. Theoretical Computer Science, 37, pp. 77- 21, 1985.

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J. A. Bergstra and J. W. Klop. Algebra of communicating processes with abstraction. Theoret. Comput. Sci., 37:77--121, 1985.

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J.A. Bergstra and J.W. Klop. Algebra of Communicating Processes with Abstraction. Theoretical Computer Science, 37, pp. 77- 21, 1985.

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J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science 37(1):77--121, 1985.

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J. Bergstra and J. Klop. Algebra of communicating processes with abstraction. Theoretical Computuper Science, 37:77--121, 1985.

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J.A. Bergstra and J.W. Klop. Algebra of Communicating Processes with Abstraction. Theoretical Computer Science, 37:77--121, 1985.

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Bergstra, J.A. and Klop, J.W. (1985), Algebra for communicating processes with abstraction. Theoretical Computer Science 37, pp77--121.

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J. Bergstra and J. Klop. Algebra for communicating processes with abstraction. Theoretical Computer Science, (37):77121, 1985.

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J.A. Bergstra and J.W. Klop, Algebra of communicating processes with abstraction, Theoretical Computer Science 37 (1985), 77--121.

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J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoret. Comp. Sci., 37:77--121, 1985.

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Bergstra, J.A. and Klop, J.W. (1985), Algebra for communicating processes with abstraction. Theoretical Computer Science 37, pp77--121.

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J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77--121, 1985.

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J. Bergstra and J. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37:77--121, 1985.

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J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77--121, 1985.

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Bergstra, J.A. and Klop, J.W. (1985), Algebra for communicating processes with abstraction. Theoretical Computer Science 37, pp77--121.

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J.A. Bergstra and J.W. Klop. Algebra for communicating processes with abstraction. Theoretical Computer Science, 37(1):77--121, 1985.

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J.A. Bergstra, J.W. Klop, Algebra of Communicating Processes with Abstraction, Theoretical Computer Science 37 (1985) 77-121

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J. A. Bergstra and J. W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37(1):77--121, 1985.

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J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37:77--121, 1985.

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Jan A. Bergstra and Jan Willem Klop. Algebra of communicating processes with abstraction. Theoretical Computer Science, 37:77-121, 1985.

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J.A. Bergstra and J.W. Klop. Algebra of communicating processes with abstraction. Theoret. Comp. Sci., 37:77--121, 1985.

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J.A. Bergstra and J.W. Klop, Algebra of communicating processes with abstraction, Theoretical Computer Sciccc 37(1), 77 121 (1985).

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