J. d. Bakker and J. Zucker, Processes and the denotational semantics of concurrency, Information and Control, 54 (1982), pp. 70-- 120.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....and specification languages. In particular, because of its intuitive appeal and flexibility, SOS has found considerable application in the study of the semantics of concurrent processes, where, despite successful work by, among others, de Bakker, Zucker, Hennessy, and Abramsky (see, e.g. [1, 31, 117, 120, 122, 125, 150]) the methods of denotational semantics appear to be difficult to apply in general. SOS generates a labelled transition system, whose states are the closed terms over an algebraic signature, and whose transitions between states are obtained inductively from a collection of so called transition ....

J. d. Bakker and J. Zucker, Processes and the denotational semantics of concurrency, Information and Control, 54 (1982), pp. 70-- 120.

....1 (m) oe 2 (m) Notice that always n 6= 0 (because we define the distance only between paths that start with the same state) and that the distance between two paths is always between 0 and 1. The idea of viewing a set of executions of a concurrent program as a metric space appears already in [AN80, BZ82], in the context of semantics of concurrent programs. Let M = S; u; l; R be a model. It can be easily shown that for every s 2 S, P s ; d) is a complete metric space. 9 Definition 3.4 Let s 2 S; n 2 N . The n environment of a path oe 2 P s (notation: n env(oe) is defined as follows: if n ....

J. W. Bakker and J. I. Zucker. Processes and the denotational semantics of concurrency. Information and Control, 54:70--120, 1982.

....is also true. Unfortunately, in order to get an identity like S PkQ = Phi(S P ; SQ ) where S P is some mathematical object representing the meaning of P , one is obliged to consider rather complex mathematical objects; furthermore, the semantical function Phi is also complex (see e.g. [9, 29]) From the particular, without toil , point of view adopted in this paper, complex objects are disallowed. As a consequence, we cannot introduce a rule for establishing the validity of triples like fAg PkQ fBg . This prevents us from introducing the operator k for parallel composition of ....

J.W. de Bakker and J.I. Zucker, Processes and the Denotational Semantics of Concurrency, Information and Control 54 (1982) 70-120.

....reductions to occur at the same time. The more complex operational semantics O s and the denotational semantics Den have no counterpart in [Br90] FLP84] and [Mo81] Although they are of classical metric inspiration, these last two semantics still present some originality with related work ([BZ82], B91] KR90] BKPR89] It arises essentially from the three following points : i) our concern with generalized Horn clauses, which has not been done before and which requires new solutions; in particular, it should be noticed that the form of communication provided by the Pi and ....

....Let Sterm be the set composed of the element fail and constructs of the form succ( Theta) where Theta is a set of substitutions. The set of denotational histories Sdhist is defined as the solution of the following recursive equation: Sdhist = Sterm[Ssusp[M n (Ssubst [ SHY P ) Theta Sdhist (see [BZ82] or [AR88] for the resolution of this equation) Histories are thus streams written as (e 1 ; e 2 ; e 3 ; Delta Delta Delta ) thanks to the cartesian products. They are often rewritten in the simpler form e 1 :e 2 :e 3 : Delta Delta Delta to avoid the intricate use of brackets. They are ....

[Article contains additional citation context not shown here]

de Bakker J.W., Zucker J.I., Processes and the Denotational Semantics of Concurrency, Information and Control 54, 1982, pp.70-120.

....critical region p. The action oe : p can be viewed as an entry accept. 9. X:p expresses infinite repetition of the atomic actions of p. 3 The Semantic Domain Two major approaches modeling processes as tree structures have been proposed. Metric spaces are used to build semantic domains in [3, 2]. One serious drawback of this approach is that sequential composition is restricted to processes whose trees are full trees (i.e. all branches are of the same depth) Such a restriction was implicitly motivated by the need to preserve monotonicity of the sequential composition operator. Indeed, ....

J.W. de Bakker and J.I. Zucker. Processes and the denotational semantics of concurrency. Information and Control, 54:70--120, 1982.

.... of termination flags as ft; ntg: 4) Define the sets Sghist and Sphist of denotational histories as the solutions of the following recursive equations Sghist = Sstate (Sterm [ Sstate Theta Sghist) Sphist = Sstate (Sterm [ Sf lag Theta Sstate Theta Sphist) respectively (see [1] or [8] for the resolution of these equations) Denotational histories are thus essentially streams written as (ss 1 ; ss 2 ; ss 3 ; Delta Delta Delta) and (ff 1 ; ss 1 ; ff 2 ; ss 2 ; ff 3 ; ss 3 ; Delta Delta Delta) thanks to the Cartesian products. They are often rewritten in the ....

J.W. de Bakker and J.I. Zucker. Processes and the Denotational Semantics of Concurrency. Information and Control, 54:70--120, 1982.

.... (PEPA) originally introduced by Hillston [8] Starting with the standard operational semantics given in terms of a transition system and strong equivalence, we provide the calculus with a denotational metric space semantics derived following the techniques introduced by de Bakker and Zucker [3] and developed in [11] We show the semantics to be fully abstract with respect to strong equivalence. The motivation behind PEPA is to introduce compositionality into the calculus, allowing processes to be composed of components by means of operators. However, this compositionality is present ....

....possible resultant components or processes the component or process will become. The difference is that for components, the values are rates, where as 5 for processes, the values are values of a probabilistic distribution. Using the metric space construction of [11] based on the methodology of [3], if we can find a metric on the set of functions from components to rates (to play the role of a metric on the set of probability distributions on processes in [11] we can construct a metric semantics for PEPA using similar techniques. Before this can be done, we first need to consider the set ....

[Article contains additional citation context not shown here]

J.W.de Bakker and J.I.Zucker. Processes and the denotational semantics of concurrency, Information and Control, vol.1/2, 1984.

....was introduced in Park [41] Bisimulation equivalence is a refinement of observational equivalence, as introduced by Hennessy Milner in [27] On the domain of finitely branching, concrete, sequential processes, both equivalences coincide. Also the semantics of De Bakker Zucker, presented in [9], coincides with bisimulation semantics on this domain. Then there are ten semantics in between. First of all a variant of trace semantics can be obtained by using complete traces besides partial ones. In this paper it is called completed trace semantics. Failures semantics is introduced in ....

....In fact the axiom amounts to saying that systems of equations like the one above have unique solutions. In [4] there is also a section on communicating systems. There two processes are identified iff they are branching equivalent. A similar idea underlies the semantics of De Bakker Zucker [9], but there the domain of processes is a complete metric space and the definition of B above only works for finitely branching processes, and only if = is interpreted as isometry, rather then equality, in order to stay in wellfounded set theory. For finitely branching processes the semantics of De ....

J.W. de Bakker & J.I. Zucker (1982): Processes and the denotational semantics of concurrency. Information and Control 54(1/2), pp. 70--120.

....of the Amsterdam Concurrency Group [BR92] In the literature, one encounters two main classes of metric domains: linear domains and branching domains. Linear domains were already studied by topologists in the early twenties. Branching domains have been introduced by, e.g. De Bakker and Zucker [BZ82, BZ83], Golson and Rounds [GR83, Gol84] and the author [Bre93] The elements of these linear and branching domains are convenient to model one might even say that they represent trace equivalence classes and bisimulation equivalence classes, respectively. The former is a simple observation. The ....

J.W. de Bakker and J.I. Zucker. Processes and the Denotational Semantics of Concurrency. Information and Control, 54(1/2):70--120, July/August 1982.

....monics, then the terminal sequence of T converges. An obvious question relating to the second theorem is whether one can drop the hypothesis that T preserves monics. One application of the rst result is to compare metric semantics for processes and data types in the style of de Bakker and Zucker [5], and America and Rutten [4] to set theoretic semantics given via terminal coalgebras. For instance, the metric approach to the semantics of nitely branching processes involves solving an equation like X = co X , where co is the compact metric powerdomain functor on the category of ....

J. de Bakker and J. Zucker, Processes and the denotational semantics of concurrency. Information and control, 54, pp70-120.

....of the atomic actions and program constructors of the language in some semantic domain. In order to deal with recursion, the domains should allow the construction of (least) fixed points. One therefore considers domains that are complete partial orders [Sco76, Plo81a] or complete metric spaces [dBZ82]. If one wants to model uniform languages, 1 one typically uses a domain specified by a recursive domain equation like P = P (fffig A A Theta P) Here A is the set of atomic actions and ffi 62 A is a special constant coding the denotation of the deadlocked process. These kinds of ....

J.W. de Bakker and J.I. Zucker. Processes and the denotational semantics of concurrency. Information and Control, 54:70--120, 1982.

....use of a semantic variant of the considered program P that allows several independent reductions to occur at the same time. The denotational semantics Den has no counterpart in [3] 10] and [16] Although it is of classical metric inspiration, it still presents some originality with related work ([6], 5] 14] which arises essentially from the two following points : i) our concern with extended Horn clauses, which has not been done before and which requires new solutions; in particular, it should be noticed that the form of communication provided by the Pi and operators ....

....fail and constructs of the form succ( Theta) where Theta is a set of substitutions. The set of denotational histories, Sdhist is defined as the solution of the following recursive equation: Sdhist = Sterm [ Ssusp [ Ssubst Theta Sdhist) Shyp Theta Ssubst Theta Sdhist) Theta Sdhist (see [6] or [1] for the resolution of this equation) Histories are thus streams written as (e 1 ; e 2 ; e 3 ; Delta Delta Delta) thanks to the cartesian products. They are often rewritten in the simpler form e 1 :e 2 :e 3 : Delta Delta Delta to avoid the intricate use of brackets. However, ....

[Article contains additional citation context not shown here]

J.W. de Bakker and J.I. Zucker. Processes and the Denotational Semantics of Concurrency. Information and Control, 54:70--120, 1982.

....functor, N a (metric) domain and M is the domain defined by the equation. Recursive domain equations are solved up to isomorphism, yielding instead the domain equation (or more accurately a domain isometry) M F(M ) The method of solving recursive domain equations over metric spaces comes from [7], 1] and [26] First some basic notions is introduced and then the functors used are given. More on domain equations can be found in e.g. 6] Definition 4.1 Let CUMS denote the category of all complete ultra metric spaces with non expansive functions as morphisms. a) A functor F : CUMS ....

J.W. de Bakker and J.I. Zucker. Processes and the denotational semantics of concurrency. Information and Control, 54:70--120, 1982.

....argue the usefulness of metric characterizations for formally reasoning about program properties. A new denotational semantics of contextual logic programs is proposed. It is defined compositionally, without any help of any declarative paradigm and of any transition system. Following the lines of [7], it uses metric spaces rather than cpo s and processes as semantic domains. It is shown to be well suited to tackle extra logical features and abstract enough for program analysis. A methodology of program analysis is derived from the denotational metric charaterization of programs. It is ....

....programs has been developed next. The denotational semantics, issued from the metric branch of the imperative approach to semantic design, is of a compositional nature and rests on no declarative framework and on no transition system. Rather, it is based on processes similar to those introduced in [7]. In contrast with declarative semantics, it is well suited to tackling extra logical features as well as infinite derivations. Although it necessarily reflects some operational behaviours, it is also more abstract than step operational semantics directly derived from transition systems. We ....

J.W. de Bakker and J.I. Zucker. Processes and the Denotational Semantics of Concurrency. Information and Control, 54:70--120, 1982.

....failed. In the next section we look at relaxation of equality, which will give us a more powerful set of tools to attack the problem posed here. 3. The Distance between DI Processes We use a distance function (metric) to relax equality. The use of metrics in process algebras is not new [Niv79, dBZ82, GR83] However, previous work concentrated on uniqueness of fixpoints, and we have seen in the previous section that this is not enough to achieve our purpose of linear derivations. A metric ae on processes is a function with the following properties. ae(x; y) 0 j x = y (13) ae(x; y) 0 (14) ....

J.W. de Bakker and J.I. Zucker. Processes and the denotational semantics of concurrency. Information and Control, 54:70--120, 1982.

....of the Amsterdam Concurrency Group [BR92] In the literature, one encounters two main classes of metric domains: linear domains and branching domains. Linear domains were already studied by topologists in the early twenties. Branching domains have been introduced by, e.g. De Bakker and Zucker [BZ82, BZ83], Golson and Rounds [GR83, Gol84] and the author [Bre93] The elements of these linear and branching domains are convenient to model one might even say that they represent trace equivalence classes and bisimulation equivalence classes, respectively. The former is a simple observation. The ....

J.W. de Bakker and J.I. Zucker. Processes and the Denotational Semantics of Concurrency. Information and Control, 54(1/2):70--120, July/August 1982.

.... The operational semantics of this language is given in terms of the probabilistic transition systems and probabilistic bisimulation of Larsen Skou [14] The calculus is provided with a denotational, metric space semantics derived following the techniques introduced by de Bakker Zucker [5] for the non probabilistic case. We show the semantics to be fully abstract with respect to the probabilistic bisimulation. Our result can be seen as complementing the framework of Larsen Skou who (without considering a calculus) give a logical characterization of probabilistic bisimulation in ....

....to ours, it does not satisfy the axioms of a metric. We omit most details of the proofs from this version of the paper. 2 Probabilistic Transition Systems and Bisimulation We assume the reader has some knowledge of metric spaces and the methodology for metric denotational semantics (see e.g. [5]) Let D be a set. A probability distribution with countable support on D is a function f : D Gamma [0; 1] such that the set s(f) fd 2 D j f(d) 0g is countable and P d2D f(d) 1. Unless otherwise stated, by a probability distribution we shall mean a probability distribution with ....

[Article contains additional citation context not shown here]

J.W.de Bakker and J.I.Zucker. Processes and the denotational semantics of concurrency, Information and Control, 1/2, 1984.

....the word process refers to the denotation of a concurrent program (or statement, or state) especially in those contexts where parallelism is reduced to non determinism sequentiality. Processes have been defined, or described, in the following three settings: Complete Metric Spaces (cms s) [5, 3]; Partial Orders (cpo s) 12, 1, 11] Non Wellfounded Sets (hypersets) 2, 13] A completely satisfactory analysis of the expressive power of these approaches has not yet been carried out. This paper focuses on the description of processes as hypersets and on the relationship between semantics ....

....as elements of the class X which is the greatest solution of the equation X = P(A Theta X) in ZFC Gamma 0 (U) FCU , where the set of actions A consists of atoms. Assuming suitable guardedness conditions, an equivalent branching time semantics is definable also using metric spaces, see [5]. In this case the domain of processes is the solution of the equation X = P co (A Theta X 1 2 ) in the category of complete metric spaces and non distance increasing functions [3] 6 Therefore, in the cases 5 A bisimulation is a relation R s.t. R (R) U , where (R) U = f(x; y) j ....

[Article contains additional citation context not shown here]

J. W. de Bakker, J. I. Zucker, Processes and the Denotational Semantics of Concurrency, Information and Control, 54:70--120, 1982.

....equivalence. The format imposes additional requirements on Groote s ntyft format. It extends an earlier format by Bloom with standard notions such as recursion, iteration, predicates, and negative premises. 1 Introduction Structural operational semantics [29] and denotational semantics [6] have evolved as the two standard methodologies to provide specification languages, programming languages, and process algebras with a semantics. In structural operational semantics, transitions between states are derived from inductive proof rules, called transition rules, which together make up ....

J.W. de Bakker and J.I. Zucker. Processes and the denotational semantics of concurrency. Information and Control, 54(1/2):70--120, 1982.

....of probabilistic choice. Starting with the standard operational semantics for PEPA, given in terms of a multi transition system and strong equivalence, we aim to provide the calculus with a denotational metric space semantics, derived following the techniques introduced by de Bakker and Zucker [1], which is fully abstract with respect to strong equivalence. The motivation behind PEPA is to introduce compositionality into the calculus, allowing processes to be composed from components by means of operators. However, this compositionality is present only at the level of syntax: once the ....

.... of methods similar to those used in [15] that there exists a largest strong equivalence relation denoted = The relation = is a congruence for PEPA, and is sufficient to ensure that equivalent components exhibit exactly the same behaviour [9] 3 Defining Metric Denotational Semantics In [1] de Bakker and Zucker introduce methodology based on the theory of metric spaces, by means of which given a (process) language one can derive a domain equation defining denotations for terms of that language. We illustrate their approach with the help of a simple example. Consider the language ....

[Article contains additional citation context not shown here]

J.W.de Bakker and J.I. Zucker. Processes and the denotational semantics of concurrency, Information and Control, 1/2:70-120, 1984.

....In the summer of 1981, De Bakker visited Zucker at Bar Ilan University. Inspired by Nivat s work, they addressed the following question: Can metric spaces be used in denotational semantics of concurrency Several visits of Zucker to Amsterdam followed and led to various publications including [BZ82]. In the latter paper, metric spaces were successfully exploited to give denotational semantics to various languages with concurrency. Besides showing that metric spaces can be used for that purpose, De Bakker and Zucker also demonstrated in [BZ82] how to solve recursive equations over metric ....

....followed and led to various publications including [BZ82] In the latter paper, metric spaces were successfully exploited to give denotational semantics to various languages with concurrency. Besides showing that metric spaces can be used for that purpose, De Bakker and Zucker also demonstrated in [BZ82] how to solve recursive equations over metric spaces. Amongst others, they solved the equation X = P c (A Theta 1 2 Delta X) where A is a set endowed with discrete metric, 1 2 Delta multiplies the metric of a metric space by a half, and P c denotes the set of closed subsets of a metric ....

[Article contains additional citation context not shown here]

J.W. de Bakker and J.I. Zucker. Processes and the Denotational Semantics of Concurrency. Information and Control, 54(1/2):70--120, July/August 1982.

....(M 1 ) P nc (M 2 ) given by F (X) f f(x) j x 2 X g is well defined and also nonexpansive. Apart from the comprehensive [BV96] mentioned earlier, the reader may consult the following introductory literature for a more extensive explanation of the use of metric spaces for semantical modeling: [BZ82, BR92, BV98]. 3 Syntax and operational semantics In this section the syntax for the language L ref with action refinement is given. Using configurations which can store refinement sequences, the notion of action refinement can be captured intuitively by a transition system. The operational semantics is ....

J.W. de Bakker and J.I. Zucker. Processes and the denotational semantics of concurrency. Information and Control, 54:70--120, 1982.

No context found.

J. W. de Bakker and J. I. Zucker. Processes and the denotational semantics of concurrency. Information and Control, 1#2, 1984.

No context found.

J.W. de Bakker and J.I. Zucker. Processes and the denotational semantics of concurrency. Information and Control, 54(1/2):70--120, 1982.

No context found.

J.W. de Bakker and J.I. Zucker. Processes and the denotational semantics of concurrency. Information and Control, 54(1/2):70--120, 1982.

First 50 documents

Online articles have much greater impact   More about CiteSeer.IST   Add search form to your site   Submit documents   Feedback  

CiteSeer.IST - Copyright Penn State and NEC