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Bisimulation for general stochastic hybrid systems
 In HSCC 2005
, 2005
"... Abstract. In this paper we define a bisimulation concept for some very general models for stochastic hybrid systems (general stochastic hybrid systems). The definition of bisimulation builds on the ideas of Edalat and of Larsen and Skou and of Joyal, Nielsen and Winskel. The main result is that this ..."
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Cited by 10 (6 self)
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Abstract. In this paper we define a bisimulation concept for some very general models for stochastic hybrid systems (general stochastic hybrid systems). The definition of bisimulation builds on the ideas of Edalat and of Larsen and Skou and of Joyal, Nielsen and Winskel. The main result is that this bisimulation for GSHS is indeed an equivalence relation. The secondary result is that this bisimulation relation for the stochastic hybrid system models used in this paper implies the same kind of bisimulation for their continuous parts and respectively for their jumping structures.
Approximating Continuous Markov Processes
, 2000
"... Markov processes with continuous state spaces arise in the analysis of stochastic physical systems or stochastic hybrid systems. The standard logical and algorithmic tools for reasoning about discrete (finitestate) systems are, of course, inadequate for reasoning about such systems. In this work we ..."
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Cited by 9 (3 self)
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Markov processes with continuous state spaces arise in the analysis of stochastic physical systems or stochastic hybrid systems. The standard logical and algorithmic tools for reasoning about discrete (finitestate) systems are, of course, inadequate for reasoning about such systems. In this work we develop three related ideas for making such reasoning principles applicable to continuous systems. ffl We show how to approximate continuous systems by a countable family of finitestate probabilistic systems, we can reconstruct the full system from these finite approximants, ffl we define a metric between processes and show that the approximants converge in this metric to the full process, ffl we show that reasoning about properties definable in a rich logic can be carried out in terms of the approximants. The systems that we consider are Markov processes where the state space is continuous but the time steps are discrete. We allow such processes to interact with the environment by syn...
A computable approach to measure and integration theory
"... We introduce a computable framework for Lebesgue’s measure and integration theory in the spirit of domain theory. For an effectively given second countable locally compact Hausdorff space and an effectively given finite Borel measure on the space, we define a recursive measurable set, which extends ..."
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Cited by 1 (0 self)
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We introduce a computable framework for Lebesgue’s measure and integration theory in the spirit of domain theory. For an effectively given second countable locally compact Hausdorff space and an effectively given finite Borel measure on the space, we define a recursive measurable set, which extends the corresponding notion due to ˜Sanin for the Lebesgue measure on the real line. We also introduce the stronger notion of a computable measurable set, where a measurable set is approximated from inside and outside by sequences of closed and open subsets respectively. The set of recursive measurable subsets and that of computable measurable subsets are both closed under complementation, finite unions and finite intersections. We then introduce intervalvalued measurable functions and develop the notion of recursive and computable measurable functions using intervalvalued simple functions. This leads us to the interval versions of the main results in classical measure theory. The Lebesgue integral is shown to be a continuous operator on the domain of intervalvalued measurable functions and the intervalvalued Lebesgue integral provides a computable framework for integration: The Lebesgue integral of a bounded recursive or computable measurable function with respect to an effectively given finite Borel measure on an effectively given locally compact second countable Hausdorff space can be computed up to any required accuracy. Key Words: Domain theory, data type, recursive and computable measurable set, intervalvalued measurable function, intervalvalued Lebesgue integral. Double Dedication: This paper is dedicated to the historical memory of Jamshid Kashani (d. 1429), the Iranian mathematician who was the first to use the recursive fixed point method in analysis with which he computed sin1 ◦ correct to 9 sexagesimal places; he is also wellknown for computing π to 16 decimal places [3, pages 7 and 151]. This work is also dedicated to my colleague and friend Giuseppe Longo on the occasion of his sixtieth birthday to commend him for his wide range of interdisciplinary research interests and for his internationalist outlook on human culture. 1.
Abstractions of Stochastic Hybrid Systems
, 2008
"... In this paper we define a stochastic bisimulation concept for a very general class of stochastic hybrid systems, which subsumes most classes of stochastic hybrid systems. The definition of this bisimulation builds on the concept of zigzag morphism defined for strong Markov processes. The main result ..."
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In this paper we define a stochastic bisimulation concept for a very general class of stochastic hybrid systems, which subsumes most classes of stochastic hybrid systems. The definition of this bisimulation builds on the concept of zigzag morphism defined for strong Markov processes. The main result is that this stochastic bisimulation is indeed an equivalence relation. The secondary result is that this bisimulation relation for the stochastic hybrid system models used in this paper implies the same kind of bisimulation for their continuous parts and respectively for their jumping structures.