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13
Bisimulation for Probabilistic Transition Systems: A Coalgebraic Approach
, 1998
"... . The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a ..."
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Cited by 75 (15 self)
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. The notion of bisimulation as proposed by Larsen and Skou for discrete probabilistic transition systems is shown to coincide with a coalgebraic definition in the sense of Aczel and Mendler in terms of a set functor. This coalgebraic formulation makes it possible to generalize the concepts to a continuous setting involving Borel probability measures. Under reasonable conditions, generalized probabilistic bisimilarity can be characterized categorically. Application of the final coalgebra paradigm then yields an internally fully abstract semantical domain with respect to probabilistic bisimulation. Keywords. Bisimulation, probabilistic transition system, coalgebra, ultrametric space, Borel measure, final coalgebra. 1 Introduction For discrete probabilistic transition systems the notion of probabilistic bisimilarity of Larsen and Skou [LS91] is regarded as the basic process equivalence. The definition was given for reactive systems. However, Van Glabbeek, Smolka and Steffen s...
Metrics for Labelled Markov Systems
, 2001
"... The notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions. Thus, a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent. This instability is due to the quantitative nature of ..."
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Cited by 48 (10 self)
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The notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions. Thus, a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent. This instability is due to the quantitative nature of probabilistic processes. In a situation where the process behaviour has a quantitative aspect there should be a more robust approach to process equivalence. This paper studies a metric between labelled Markov processes. This metric has the property that processes are at zero distance if and only if they are bisimilar. The metric is inspired by earlier work on logics for characterizing bisimulation and is related, in spirit, to the Hutchinson metric.
Metrics for Labelled Markov Processes
, 2003
"... The notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions. Thus, a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent. This instability is due to the quantitative nature ..."
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Cited by 45 (10 self)
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The notion of process equivalence of probabilistic processes is sensitive to the exact probabilities of transitions. Thus, a slight change in the transition probabilities will result in two equivalent processes being deemed no longer equivalent. This instability is due to the quantitative nature of probabilistic processes. In a situation where the process behaviour has a quantitative aspect there should be a more robust approach to process equivalence. This paper studies a metric between labelled Markov processes. This metric has the property that processes are at zero distance if and only if they are bisimilar. The metric is inspired by earlier work on logics for characterizing bisimulation and is related, in spirit, to the Kantorovich metric.
Domain Equations for Probabilistic Processes
 In Proc. Express'97. Electronic Notes in Theoretical Computer Science 7
, 1997
"... ) Christel Baier Fakultat fur Mathematik & Informatik Universitat Mannheim 68131 Mannheim, Germany Marta Kwiatkowska 1 School of Computer Science University of Birmingham Edgbaston, Birmingham B15 2TT, UK Abstract In this paper we consider Milner's calculus CCS enriched by a probabilistic choice ..."
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Cited by 16 (1 self)
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) Christel Baier Fakultat fur Mathematik & Informatik Universitat Mannheim 68131 Mannheim, Germany Marta Kwiatkowska 1 School of Computer Science University of Birmingham Edgbaston, Birmingham B15 2TT, UK Abstract In this paper we consider Milner's calculus CCS enriched by a probabilistic choice operator. The calculus is given operational semantics based on probabilistic transition systems. We define operational notions of preorder and equivalence as probabilistic extensions of the simulation preorder and the bisimulation equivalence respectively. We extend existing categorytheoretic techniques for solving domain equations to the probabilistic case and give two denotational semantics for the calculus. The first, "smooth", semantic model arises as a solution of a domain equation involving the probabilistic powerdomain and solved in the category CONT? of continuous domains. The second model also involves appropriately restricted probabilistic powerdomain, but is constructed in the c...
PROBMELA: a modeling language for communicating probabilistic processes
, 2004
"... Building automated tools to address the analysis of reactive probabilistic systems requires a simple, but expressive input language with a formal semantics based on a probabilistic operational model that can serve as starting point for verification algorithms. We introduce a higher level description ..."
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Cited by 10 (3 self)
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Building automated tools to address the analysis of reactive probabilistic systems requires a simple, but expressive input language with a formal semantics based on a probabilistic operational model that can serve as starting point for verification algorithms. We introduce a higher level description language for probabilistic parallel programs with shared variables, message passing via synchronous and (perfect or lossy) fifo channels and atomic regions and provide a structured operational semantics. Applied to finitestate systems, the semantics can serve as basis for the algorithmic generation of a Markov decision process that models the stepwise behavior of the given system.
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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Cited by 7 (1 self)
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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.
Mixing Up Nondeterminism and Probability: a preliminary report
, 1999
"... For a process language with both nondeterministic and probabilistic choice, and a form of failure a transition system is given from which, in a modular way, various operational models corresponding to various interpretations of nondeterminism and probability can be obtained. The effect of failure of ..."
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Cited by 6 (4 self)
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For a process language with both nondeterministic and probabilistic choice, and a form of failure a transition system is given from which, in a modular way, various operational models corresponding to various interpretations of nondeterminism and probability can be obtained. The effect of failure of one component for the system as a whole is treated differently in each interpretation. The same approach is followed for an extension of the language with a parallel operator. The adopted concurrency model is of a distributed nature and assumes that progress is guaranteed if nonfailing components exist. To this end the notion of a takeover of a failing component is incorporated in the transition system. It is shown that the modular way in which the transition system can yield different semantical models applies to this setting as well.
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
Comparative Semantics for a Process Language With Probabilistic Choice and NonDeterminism
, 1998
"... In this report a comparative semantics is given for a language L p containing probabilistic and nondeterministic choice. The effects of interpreting these operators as local or global are investigated. For three of the possible combinations an operational model and a denotational model are given an ..."
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Cited by 3 (2 self)
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In this report a comparative semantics is given for a language L p containing probabilistic and nondeterministic choice. The effects of interpreting these operators as local or global are investigated. For three of the possible combinations an operational model and a denotational model are given and compared. First models for local probabilistic choice and local nondeterministic choice are given using a generative approach. By adjusting these models slightly models for global probability and local nondeterminism are obtained. Finally models for local probability and global nondeterminism are presented using a stratified approach. For use with the denotational models a construction of a complete ultrametric space of finite multisets is given. 1 Introduction The goal of this paper is to construct comparative semantics for a language combining nondeterminism and probabilistic choice. The main interest is the interplay between these two concepts. Since many of the interesting proper...
Proving Approximate Implementations for Probabilistic I/O Automata?? Abstract
, 2006
"... In this paper we introduce the notion of approximate implementations for Probabilistic I/O Automata (PIOA) and develop methods for proving such relationships. We employ a task structure on the locally controlled actions and a task scheduler to resolve nondeterminism. The interaction between a schedu ..."
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Cited by 2 (0 self)
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In this paper we introduce the notion of approximate implementations for Probabilistic I/O Automata (PIOA) and develop methods for proving such relationships. We employ a task structure on the locally controlled actions and a task scheduler to resolve nondeterminism. The interaction between a scheduler and an automaton gives rise to a trace distribution—a probability distribution over the set of traces. We define a PIOA to be a (discounted) approximate implementation of another PIOA if the set of trace distributions produced by the first is close to that of the latter, where closeness is measured by the (resp. discounted) uniform metric over trace distributions. We propose simulation functions for proving approximate implementations corresponding to each of the above types of approximate implementation relations. Since our notion of similarity of traces is based on a metric on trace distributions, we do not require the state spaces nor the space of external actions of the automata to be metric spaces. We discuss applications of approximate implementations to verification of probabilistic safety and termination.