253 research outputs found

    Metric semantics for concurrency

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    Metric Semantics and Full Abstractness for Action Refinement and Probabilistic Choice

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    This paper provides a case-study in the field of metric semantics for probabilistic programming. Both an operational and a denotational semantics are presented for an abstract process language L_pr, which features action refinement and probabilistic choice. The two models are constructed in the setting of complete ultrametric spaces, here based on probability measures of compact support over sequences of actions. It is shown that the standard toolkit for metric semantics works well in the probabilistic context of L_pr, e.g. in establishing the correctness of the denotational semantics with respect to the operational one. In addition, it is shown how the method of proving full abstraction --as proposed recently by the authors for a nondeterministic language with action refinement-- can be adapted to deal with the probabilistic language L_pr as well

    On the definability of concurrency and communication : event structures versus pomset classes

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    In the context of communicating parallel process systems various paradigma for communication resp. synchronisation have been proposed. Two well-known theoretical models for communicating systems are CCS and TCSP. A variety of semantics has been proposed for these and similar languages which can be characterized by different criteria: true versus interleaving parallelism, linear versus branching time models, operational versus denotational approaches, choice of the mathematical discipline to handle recursion and domain equations. In recent years interest has shifted more and more towards semantics that model true parallelism. The most known are petri net semantics, event structure and pomset semantics. The present paper investigates the question whether the two closely related approaches of event structures and pomsets are equally suitable to provide semantics for language constructs as avaible in CCS or TCSP. Given the variety of approaches to semantic description comparative studies like the present one are importantas a guideline. They help us to decide which method suits which purpose. In addition, comparative studies enhance the better understanding of the language constructs, and finally comparative studies of semantics that yield consistency results strengthen our confidence in the correctness of each, of the semantics involved. The paper is divided into seven sections. Section 2 introdtices CCS and TCSP and discusses their communication mechanisms. Section3 introduces event structures. Section 4 defines pomset classes. Section 5 models the communication mechanisms of CCS and TCSP using event structures and section 6 discusses the problems that arise when pomset classes are used. Section 7 is the conclusion. The appendix contains some formal definitions

    Fully abstract denotational models for nonuniform concurrent languages

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    AbstractThis paper investigates full abstraction of denotational model w.r.t. operational ones for two concurrent languages. The languages are nonuniform in the sense that the meaning of atomic statements generally depends on the current state. The first language, L1, has parallel composition but no communication, whereas the second one, L2, has CSP-like communications in addition. For each of Li (i = 1, 2), an operational model Oi is introduced in terms of a Plotkin-style transition system, while a denotational model Di for Li is defined compositionally using interpreted operations of the language, with meanings of recursive programs as fixed points in appropriate complete metric spaces. The full abstraction is shown by means of a context with parallel composition: Given two statements s1 and s2 with different denotational meanings, a suitable statement T is constructed such that the operational meanings of s1 āˆ„ T and s2 āˆ„ T are distinct. A combinatorial method for constructing such T is proposed. Thereby the full abstraction of D1 and D2 w.r.t. O1 and O2, respectively, is established. That is, Di is most abstract of those models C which are compositional and satisfy Oi = Ī± āˆ˜ C for some abstraction function Ī± (i = 1, 2)
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