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Nondeterminism and Probabilistic Choice: Obeying the Laws
 In Proc. 11th CONCUR, volume 1877 of LNCS
, 2000
"... In this paper we describe how to build semantic models that support both nondeterministic choice and probabilistic choice. Several models exist that support both of these constructs, but none that we know of satisfies all the laws one would like. Using domaintheoretic techniques, we show how models ..."
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Cited by 31 (2 self)
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In this paper we describe how to build semantic models that support both nondeterministic choice and probabilistic choice. Several models exist that support both of these constructs, but none that we know of satisfies all the laws one would like. Using domaintheoretic techniques, we show how models can be devised using the "standard model" for probabilistic choice, and then applying modified domaintheoretic models for nondeterministic choice. These models are distinguished by the fact that the expected laws for nondeterministic choice and probabilistic choice remain valid. We also describe some potential applications of our model to aspects of security.
Probabilistic metric semantics for a simple language with recursion
 Proc. Mathematical Foundations of Computer Science (MFCS), volume 1113 of Lecture Notes in Computer Science
, 1996
"... Abstract. We consider a simple divergencefree language RP for reactive processes which includes prefixing, deterministic choice, actionguarded probabilistic choice, synchronous parallel and recursion. We show that the probabilistic bisimulation of Larsen & Skou is a congruence for this language ..."
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Cited by 19 (6 self)
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Abstract. We consider a simple divergencefree language RP for reactive processes which includes prefixing, deterministic choice, actionguarded probabilistic choice, synchronous parallel and recursion. We show that the probabilistic bisimulation of Larsen & Skou is a congruence for this language. Following the methodology introduced by de Bakker & Zucker we give denotational semantics to this language by means of a complete metric space of (deterministic) probabilistic trees defined in terms of the powerdomain of closed sets. This new metric, although not an ultrametric, nevertheless specialises to the metric of de Bakker & Zucker. Our semantic domain admits a full abstraction result with respect to probabilistic bisimulation. 1
EventState Duality: The Enriched Case
"... Enriched categories have been applied in the past to both eventoriented true concurrency models and stateoriented information systems, with no evident relationship between the two. Ordinary Chu spaces expose a natural duality between partially ordered temporal spaces (pomsets, event structures), a ..."
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Cited by 7 (0 self)
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Enriched categories have been applied in the past to both eventoriented true concurrency models and stateoriented information systems, with no evident relationship between the two. Ordinary Chu spaces expose a natural duality between partially ordered temporal spaces (pomsets, event structures), and partially ordered information systems.
Metric semantics for reactive probabilistic processes
, 1997
"... In this thesis we present three mathematical frameworks for the modelling of reactive probabilistic communicating processes. We first introduce generalised labelled transition systems as a model of such processes and introduce an equivalence, coarser than probabilistic bisimulation, over these syst ..."
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Cited by 6 (1 self)
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In this thesis we present three mathematical frameworks for the modelling of reactive probabilistic communicating processes. We first introduce generalised labelled transition systems as a model of such processes and introduce an equivalence, coarser than probabilistic bisimulation, over these systems. Two processes are identified with respect to this equivalence if, for all experiments, the probabilities of the respective processes passing a given experiment are equal. We next consider a probabilistic process calculus including external choice, internal choice, actionguarded probabilistic choice, synchronous parallel and recursion. We give operational semantics for this calculus be means of our generalised labelled transition systems and show that our equivalence is a congruence for this language. Following the methodology introduced by de Bakker & Zucker, we then give denotational semantics to the calculus by means of a complete metric space of probabilistic processes. The derived metric, although not an ultrametric, satisfies the intuitive property that the distance between two processes tends to 0 if a measure of the dif
A Fully Abstract MetricSpace Denotational Semantics for Reactive Probabilistic Processes
 In Proc. COMPROX '98, Electronic Notes in TCS vol.13
, 1998
"... MetricSpace Denotational Semantics for Reactive Probabilistic Processes M.Z. Kwiatkowska and G.J. Norman School of Computer Science, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Abstract We consider the calculus of Communicating Sequential Processes (CSP) [8] extended with act ..."
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MetricSpace Denotational Semantics for Reactive Probabilistic Processes M.Z. Kwiatkowska and G.J. Norman School of Computer Science, University of Birmingham, Edgbaston, Birmingham B15 2TT, UK Abstract We consider the calculus of Communicating Sequential Processes (CSP) [8] extended with actionguarded probabilistic choice and provide it with an operational semantics in terms of a suitable extension of Larsen and Skou's [14] reactive probabilistic transition systems. We show that a testing equivalence which identi es two processes if they pass all tests with the same probability is a congruence for a subcalculus of CSP including external and internal choice and the synchronous parallel. Using the methodology of de Bakker and Zucker [3] introduced for classical process calculi, we derive a metricspace semantic model for the calculus and show it is fully abstract.
Iteration monads
 Proceedings CMCS'01. Electronic Notes in Theoretical Computer Science 44
, 2001
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On Coalgebras and Final Semantics: Progress Report
"... This report summarises research undertaken by the author as part of his DPhil in computation. A draft table of contents of the thesis, a proposed timetable for submission, and a list of publications are also included. ..."
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This report summarises research undertaken by the author as part of his DPhil in computation. A draft table of contents of the thesis, a proposed timetable for submission, and a list of publications are also included.
Building Metric Structures with the MeasFunctor
"... We introduce the functor Meas in the category of complete ultra metric spaces and nonexpansive mapping. The main result of this paper is that Meas is a wellde ned and locally nonexpansive endofunctor. Therefore the functor ts naturally in the metric approach to programming language semantics. ..."
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We introduce the functor Meas in the category of complete ultra metric spaces and nonexpansive mapping. The main result of this paper is that Meas is a wellde ned and locally nonexpansive endofunctor. Therefore the functor ts naturally in the metric approach to programming language semantics. The use of Meas in the construction of probabilistic powerdomains, either directly or through the use of domain equations, is illustrated with two examples.