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Continuous Previsions ⋆
"... Abstract. We define strong monads of continuous (lower, upper) previsions, and of forks, modeling both probabilistic and nondeterministic choice. This is an elegant alternative to recent proposals by Mislove, Tix, Keimel, and Plotkin. We show that our monads are sound and complete, in the sense tha ..."
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Cited by 6 (4 self)
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Abstract. We define strong monads of continuous (lower, upper) previsions, and of forks, modeling both probabilistic and nondeterministic choice. This is an elegant alternative to recent proposals by Mislove, Tix, Keimel, and Plotkin. We show that our monads are sound and complete, in the sense that they model exactly the interaction between probabilistic and (demonic, angelic, chaotic) choice. 1
Approximating Markov Processes by Averaging
"... Abstract. We take a dual view of Markov processes – advocated by Kozen – as transformers of bounded measurable functions. We redevelop the theory of labelled Markov processes from this view point, in particular we explore approximation theory. We obtain three main results: (i) It is possible to defi ..."
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Cited by 1 (0 self)
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Abstract. We take a dual view of Markov processes – advocated by Kozen – as transformers of bounded measurable functions. We redevelop the theory of labelled Markov processes from this view point, in particular we explore approximation theory. We obtain three main results: (i) It is possible to define bisimulation on general measure spaces and show that it is an equivalence relation. The logical characterization of bisimulation can be done straightforwardly and generally. (ii) A new and flexible approach to approximation based on averaging can be given. This vastly generalizes and streamlines the idea of using conditional expectations to compute approximation. (iii) It is possible to show that there is a minimal bisimulation equivalent to a process obtained as the limit of the finite approximants. 1
ProjectTeam SECSI Sécurité des systèmes d’information Saclay ÎledeFrance
"... c t i v it y e p o r t ..."
ProjectTeam SECSI Sécurité des systèmes d’information
"... c t i v it y e p o r t 2007 Table of contents ..."
Approximating Markov Processes By Averaging
"... Normally, one thinks of probabilistic transition systems as taking an initial probability distribution over the state space into a new probability distribution representing the system after a transition. We, however, take a dual view of Markov processes as transformers of bounded measurable function ..."
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Normally, one thinks of probabilistic transition systems as taking an initial probability distribution over the state space into a new probability distribution representing the system after a transition. We, however, take a dual view of Markov processes as transformers of bounded measurable functions. This is very much in the same spirit as a “predicatetransformer ” view, which is dual to the statetransformer view of transition systems. We redevelop the theory of labelled Markov processes from this view point, in particular we explore approximation theory. We obtain three main results: (i) It is possible to define bisimulation on general measure spaces and show that it is an equivalence relation. The logical characterization of bisimulation can be done straightforwardly and generally. (ii) A new and flexible approach to approximation based on averaging can be given. This vastly generalizes and streamlines the idea of using conditional expectations to compute approximations. (iii) We show that there is a minimal process bisimulationequivalent to a given process, and this minimal process is obtained as the limit of the finite approximants.
Belief Functions on Formulas in Lukasiewicz Logic
"... Belief functions are generalized to formulas in Lukasiewicz logic. It is shown that they generalize probabilities on formulas (socalled states) and that they are completely monotone mappings with respect to the lattice operations. 1 ..."
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Belief functions are generalized to formulas in Lukasiewicz logic. It is shown that they generalize probabilities on formulas (socalled states) and that they are completely monotone mappings with respect to the lattice operations. 1
Concrete Semantics of Programs with NonDeterministic and Random Inputs
, 1210
"... This document gives semantics to programs written in a Clike programming language, featuring interactions with an external environment with noisy and imprecise data. 1 ..."
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This document gives semantics to programs written in a Clike programming language, featuring interactions with an external environment with noisy and imprecise data. 1
Under consideration for publication in Math. Struct. in Comp. Science ChoquetKendallMatheron Theorems for NonHausdorff Spaces
, 2010
"... We establish ChoquetKendallMatheron theorems on nonHausdorff topological spaces. This typical result of random set theory is profitably recast in purely topological terms, using intuitions and tools from domain theory. We obtain three variants of the theorem, each one characterizing distributions ..."
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We establish ChoquetKendallMatheron theorems on nonHausdorff topological spaces. This typical result of random set theory is profitably recast in purely topological terms, using intuitions and tools from domain theory. We obtain three variants of the theorem, each one characterizing distributions, in the form of continuous valuations, over relevant powerdomains of demonic, resp. angelic, resp. erratic nondeterminism. 1.
CEA LIST
"... Abstract. Having a precise yet sound abstraction of the inputs of numerical programs is important to analyze their behavior. For many programs, these inputs are probabilistic, but the actual distribution used is only partially known. We present a static analysis framework for reasoning about program ..."
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Abstract. Having a precise yet sound abstraction of the inputs of numerical programs is important to analyze their behavior. For many programs, these inputs are probabilistic, but the actual distribution used is only partially known. We present a static analysis framework for reasoning about programs with inputs given as imprecise probabilities: we semantics based on an extension of DempsterShafer structures. We prove the correctness of our approach and show on some realistic examples the kind of invariants we are able to infer. 1