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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.
A Process Algebra for Probabilistic and Nondeterministic Processes
 Information Processing Letters
, 2001
"... In this paper we present an algebraic language for the specification of probabilistic and nondeterministic processes, PNAL , which is a probabilistic extension of EPL that maintains nondeterminism. ..."
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In this paper we present an algebraic language for the specification of probabilistic and nondeterministic processes, PNAL , which is a probabilistic extension of EPL that maintains nondeterminism.
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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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
Argument duplication in probabilistic CSP
, 1995
"... In [2] a space PCSP of probabilistic processes is constructed uniformly from the standard CSP failuresdivergences model. Laws of CSP are shown to be valid in PCSP also, provided they have no duplication on either side of = or v separately: thus for example A u B = B u A carries over to PCSP; but A ..."
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Cited by 5 (2 self)
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In [2] a space PCSP of probabilistic processes is constructed uniformly from the standard CSP failuresdivergences model. Laws of CSP are shown to be valid in PCSP also, provided they have no duplication on either side of = or v separately: thus for example A u B = B u A carries over to PCSP; but AuA = A does not, because of the duplication on its lefthand side. Here we propose two devices for retaining more of CSP's laws within PCSP: the first introduces a limited form of state; the second allows multiple occurrences of a term to be abstracted to a single syntactic location. Either [2] or its published revision are prerequisites for understanding this report fully, although skimming Sec. 4 and App. A may give an idea of what has been achieved. 1 Introduction The law A u A = A fails in PCSP only when A is properly nondeterministic; and when that is so, the reason for its failure is the possibly independent resolution of probabilistic choice in the two copies. For example, (B 1 2 \...
Possibilistic and Probabilistic AbstractionBased Model Checking
 Process Algebra and Probabilistic Methods, Performance Modeling and Veri Second Joint International Workshop PAPMPROBMIV 2002, volume 2399 of Lecture Notes in Computer Science
, 2002
"... models whose verification results transfer to the abstracted models for a logic with unrestricted use of negation and quantification. This framework is novel in that its models have quantitative or probabilistic observables and state transitions. Properties of a quantitative temporal logic have meas ..."
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Cited by 4 (2 self)
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models whose verification results transfer to the abstracted models for a logic with unrestricted use of negation and quantification. This framework is novel in that its models have quantitative or probabilistic observables and state transitions. Properties of a quantitative temporal logic have measurable denotations in these models. For probabilistic models such denotations approximate the probabilistic semantics of full LTL. We show how predicatebased abstractions specify abstract quantitative and probabilistic models with finite state space. 1
Backwards abstract interpretation of probabilistic programs
 IN EUROPEAN SYMPOSIUM ON PROGRAMMING LANGUAGES AND SYSTEMS (ESOP '01), NUMBER 2028 IN LECTURE NOTES IN COMPUTER SCIENCE
, 2001
"... ..."
Hierarchical Reasoning in Probabilistic CSP
, 1996
"... Probabilistic CSP extends the language of CSP with an operator for probabilistic choice. However reasoning about an intricate combination of nondeterminism, communication and probabilistic behaviour can be complicated. In standard CSP such complication is overcome (when possible) by use of hierarchi ..."
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Probabilistic CSP extends the language of CSP with an operator for probabilistic choice. However reasoning about an intricate combination of nondeterminism, communication and probabilistic behaviour can be complicated. In standard CSP such complication is overcome (when possible) by use of hierarchical reasoning. In this paper we provide a foundation for lifting such reasoning to the probabilistic setting. First we formalise the common observation that the standard models of CSP (traces, refusals and refusals/divergences) form a hierarchy, by showing that they are linked by embeddingprojection pairs. Such structure underlies hierarchical reasoning in which complex process behaviour is reasoned about in terms of its simpler projections. Then we show how that hierarchy can be extended to a corresponding hierarchy between the probabilistic models, by using each of those three models of standard CSP as a basis for a probabilistic extension. Finally we show that there is a projection from ...
The Weakest Completion Approach to the Probabilistic Semantics
, 2000
"... A standard program starts its execution in an initial state, and terminates (if it ever does) in one of a set of final states. Its behaviour can be modelled by a binary relation between the initial and final states. The difference between the standard and the probabilistic semantics is that the form ..."
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A standard program starts its execution in an initial state, and terminates (if it ever does) in one of a set of final states. Its behaviour can be modelled by a binary relation between the initial and final states. The difference between the standard and the probabilistic semantics is that the former tells us which final states are or are not possible, whereas the latter tells us the probability with which they may occur. This paper presents a link between the probabilistic and the imperative programming using the weakest completion. We demonstrate how the probabilistic semantics can be derived directly from the standard relational one using the type embedding and healthiness condition of real programs. Carroll Morgan is an adjunct professor in the department of computer science at New South Wales University in Australia. He conducts research in the area of refinement theories and formal methods applied to software engineering and applications to parallel and distributed computing, ...
Software Technology Reasoning about a distributed probabilistic system
, 2008
"... Training Centre of the United Nations University (UNU). It is based in Macao, and was founded in 1991. It started operations in July 1992. UNUIIST is jointly funded by the government of Macao and the governments of the People’s Republic of China and Portugal through a contribution to the UNU Endowm ..."
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Training Centre of the United Nations University (UNU). It is based in Macao, and was founded in 1991. It started operations in July 1992. UNUIIST is jointly funded by the government of Macao and the governments of the People’s Republic of China and Portugal through a contribution to the UNU Endowment Fund. As well as providing twothirds of the endowment fund, the Macao authorities also supply UNUIIST with its office premises and furniture and subsidise fellow accommodation. The mission of UNUIIST is to assist developing countries in the application and development of software technology. UNUIIST contributes through its programmatic activities: 1. Advanced development projects, in which software techniques supported by tools are applied, 2. Research projects, in which new techniques for software development are investigated, 3. Curriculum development projects, in which courses of software technology for universities in developing countries are developed, 4. University development projects, which complement the curriculum development projects by aiming to strengthen all aspects of computer science teaching in universities in developing countries, 5. Schools and Courses, which typically teach advanced software development techniques,
CSP: The Best ConcurrentSystem Description Language in the World – Probably! Extended Abstract
"... Abstract. CSP, Hoare’s Communicating Sequential Processes, [1, 2] is one of the formalisms that underpins the antecedents of CPA, and this year celebrates its Silver Jubilee [3]. Formal Systems ’ own FDR refinement checker [4] is among the most powerful explicit exhaustive finitestate exploration t ..."
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Abstract. CSP, Hoare’s Communicating Sequential Processes, [1, 2] is one of the formalisms that underpins the antecedents of CPA, and this year celebrates its Silver Jubilee [3]. Formal Systems ’ own FDR refinement checker [4] is among the most powerful explicit exhaustive finitestate exploration tools, and is tailored specifically to the CSP semantics. The CSPM ASCII form of CSP, in which FDR scripts are expressed, is the defacto standard for CSP tools. Recent work has experimentally extended the notation to include a probabilistic choice construct, and added functionality into FDR to produce models suitable for analysis by the Birmingham University PRISM tool [5]. 1