J.W. de Bakker, J.A. Bergstra, et al. Linear time and branching time semantics for recursion with merge. In Automata, Languages and Programming, LNCS 154, pages 39--51. Springer-Verlag, 1983.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....of a uniform language supporting the rendezvous mechanism. The domain we construct provides a means of distinguishing processes which share the same language but which differ as to their respective choices points. In other words, we develop what is commonly known as a branching time semantics [2]. A detailed presentation of the language is given in the next section. In Section 3, we explain the structure of the domain. This will form the basis of our model. Section 4 gives definitions of the semantic function and the finite elements of the signature. Section 5 proves monotonicity and ....

....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, J.A. Bergstra, et al. Linear time and branching time semantics for recursion with merge. In Automata, Languages and Programming, LNCS 154, pages 39--51. Springer-Verlag, 1983.

....system as De Bakker, This work was carried out during a visit of BRICS, Department of Computer Science, University of Aarhus, Denmark with financial support of BRICS. y The author is supported by the Netherlands Organization for Scientific Research. 444 Bergstra, Klop, and Meyer noted in [BBKM84]. It can even be viewed as a metric labelled transition system. This metric labelled transition system is compactly branching being a generalization of finitely branching. As a consequence, we can apply a theorem being a generalization of a theorem reminiscent to Konig s lemma obtaining the ....

J.W. de Bakker, J.A. Bergstra, J.W. Klop, and J.-J.Ch. Meyer. Linear Time and Branching Time Semantics for Recursion with Merge. Theoretical Computer Science, 34(1/2):135--156, 1984.

....not have their usual meanings in boolean logic. 17. f comment g is a comment string and is used for documentation of the program. 5 3.2 The TPL Semantic Domains Two major approaches modeling processes as tree structures have been proposed. Metric spaces are used to build semantic domains in [21, 31]. One serious drawback of this approach is that sequential composition is restricted to processes whose trees are full trees, that is, all branches are of the same depth. Such a restriction was implicitly motivated by the need to preserve monotonicity of the sequential composition operator. ....

J. W. de Bakker, J. A. Bergstra, J. W. Klop, and J.-J. C. Meyer, "Linear time and branching time semantics for recursion with merge," in Automata, Languages, and Programming (J. Diaz, ed.), no. 154 in LNCS, pp. 39--51, Barcelona, Spain: Springer-Verlag, 1983.

....that each t in this row corresponds with the execution of an elementary action by the abstract machine, i.e. one iteration of the step function. Similarly for a nonterminating computation, we do not deliver but an infinite row of t s instead. So is reformulated as internal divergence, as in [BBKM]) Now, for the corresponding meaning functions O and D a compact equivalence proof can be given. In order to establish from this the equivalence of our original functions O and D it is sufficient to show that there exists an abstraction operator strip, a t remover so to speak, such that ....

J.W. de Bakker, J.A. Bergstra, J.W. Klop, and J.-J.Ch Meyer, "Linear Time and Branching Time Semantics for Recursion with Merge," Theoretical Computer Science 34, pp. 135-156 (1984).

....applying the open maps approach of [19] to trace equivalence. One of the contributions of the present paper is to show that such a linearization stems from the distributive law between B and P. For more details on the BT and LT models of non determinism see early work on concurrency, such as, eg, [8]. Contents In Section 1 we recall some basic facts about transition systems and coalgebras. In Section 2 we define the category of coalgebras of the endofunctor B obtained by lifting the deterministic behaviour endofunctor B to the Kleisli category of the non empty powerset monad P and we ....

J.W. de Bakker, J.A. Bergstra, J.W. Klop, and J.-J. Meyer. Linear time and branching time semantics for recursion with merge. Theoretical Computer Science, 34(1-2):135--156, November 1984.

....metric labelled transition system. The theory of metric labelled transition systems has been outlined in the author s [Bre94a] and has been developed further in his thesis [Bre94b] The branching domain B can be seen as a labelled transition system as De Bakker, Bergstra, Klop, and Meyer noted in [BBKM84]. It can even be viewed as a compactly branching being a generalization of finitely branching metric labelled transition system. The additional metric structure of a metric labelled transition system (with respect to a labelled transition systems) is essential in the definition of the ....

....(of the labelled transition system (C; A; and the branching processes (in the image of fix ( Psi (C;A; 3 A linearize operator The linearize operator is defined by means of the theory of (metric) labelled transition systems. As De Bakker, Bergstra, Klop, and Meyer noted in Remark 4. 3 of [BBKM84], the branching domain B can be viewed as a labelled transition system. The configurations of the labelled transition systems are the branching processes. As action set we take the set A. The transition relation is presented in Definition 3.1 The transition relation B Theta A Theta B is ....

J.W. de Bakker, J.A. Bergstra, J.W. Klop, and J.-J.Ch. Meyer. Linear Time and Branching Time Semantics for Recursion with Merge. Theoretical Computer Science, 34(1/2):135--156, November 1984.

....equivalences that are fully abstract with respect to some notion of observability. Introduction When comparing models or equivalences for concurrent systems, it is common practice to distinguish between linear time and branching time semantics (see for instance De Bakker, Bergstra, Klop Meyer [1] or Pnueli [9] In the former, a process is completely determined by the observable content of its possible (partial) runs, whereas in the latter also the information is preserved where two different courses of action diverge (although branching of identical courses of action may still be ....

J.W. de Bakker, J.A. Bergstra, J.W. Klop & J.-J.Ch. Meyer (1984): Linear time and branching time semantics for recursion with merge. Theoretical Computer Science 34, pp. 135--156.

....system as De Bakker, This work was carried out during a visit of BRICS, Department of Computer Science, University of Aarhus, Denmark with financial support of BRICS. y The author is supported by the Netherlands Organization for Scientific Research. Bergstra, Klop, and Meyer noted in [BBKM84]. It can even be viewed as a metric labelled transition system. This metric labelled transition system is compactly branching being a generalization of finitely branching. As a consequence, we can apply a theorem being a generalization of a theorem reminiscent to Konig s lemma obtaining the ....

J.W. de Bakker, J.A. Bergstra, J.W. Klop, and J.-J.Ch. Meyer. Linear Time and Branching Time Semantics for Recursion with Merge. Theoretical Computer Science, 34(1/2):135--156, 1984.

....semantical models would deliver as the meaning of the procedure x, discussed above, the maximal set t n ba n n 0 t w . One could say that the effect of these new semantical operators is that, in an artificial way, all procedure calls have been made guarded. An idea also present in [BBKM]. The equivalence of O and D will then be established by the standard metrical technique but now in the setting of cpo s. The next step to take is to define an abstraction operator r for which the equalities O = r(O ) and D = r(D ) should hold. This abstraction operator will be ....

....r( lub n x [n ] r( lub n y [n ] by continuity of r and = r(x ) r(y ) 5 Next we mimic the denotational mapping D. Note the occurrence of t in the definition of the transformation H d . This idea of guarding procedure calls with a dummy step can also be observed in the semantics of [BBKM]a. 5.5) DEFINITION Define the collection Env , with typical element h , by Env = X P (A t st ) Define the mapping S : Stat E Env P (A t st ) by S (E) h ) e , S (a ) h ) a , S (x ) h ) h (x ) S (s 1 s 2 ) h ) S (s 1 ) h ) S (s 2 ....

J.W. de Bakker, J.A. Bergstra, J.W. Klop, and J.-J.Ch. Meyer, "Linear Time and Branching Time Semantics for Recursion with Merge," Theoretical Computer Science 34, pp. 135-156 (1984).

....theory for the last two decades. This notion is due to Robin Milner and David Park [Mil80, Par81, Mil94] Not long after the introduction of De Bakker Zucker processes, several members of the Amsterdam Concurrency Group suspected that these processes are closely related to bisimulation (see, e.g. [BBKM84]) More than half a decade later, Rob van Glabbeek and Jan Rutten made this suspicion precise. In [GR89] they showed that De Bakker Zucker processes represent bisimulation equivalence classes. In the early eighties, a link between recursive equations over ordered spaces and terminal coalgebras ....

J.W. de Bakker, J.A. Bergstra, J.W. Klop, and J.-J.Ch. Meyer. Linear Time and Branching Time Semantics for Recursion with Merge. Theoretical Computer Science, 34(1/2):135--156, November 1984.

....1 ) CS(ff 2 ) where for k 1 Seq k (while do ff 1 od) f Pi k j=1 ( ff 0 j ) j ff 0 j 2 CS(ff 1 ) for j = 1; kg 5.6. Remark. The definition of the finite computation sequences of action ff is essentially identical to that of the trace set of ff using linear time semantics (cf. [BBKM84]) Note furthermore that the set of finite computation sequences of an action ff is determined by the syntactical shape of ff only. 5.7. Lemma. For all actions ff 2 Ac I we have: CS(ff) 6= Proof of lemma 5.7: By induction on the structure of ff: the cases for atomic actions, confirmations, ....

J.W. de Bakker, J.A. Bergstra, J.W. Klop, and J.-J.Ch. Meyer. Linear time and branching time semantics for recursion with merge. Theoretical Computer Science, 34:135--156, 1984.

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