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Concurrent Constraint Programming: Towards Probabilistic Abstract Interpretation
 Proc. of the 23rd International Symposium on Mathematical Foundations of Computer Science, MFCS'98, Lecture Notes in Computer Science
, 2000
"... We present a method for approximating the semantics of probabilistic programs to the purpose of constructing semanticsbased analyses of such programs. The method resembles the one based on Galois connection as developed in the Cousot framework for abstract interpretation. The main difference betwee ..."
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Cited by 20 (8 self)
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We present a method for approximating the semantics of probabilistic programs to the purpose of constructing semanticsbased analyses of such programs. The method resembles the one based on Galois connection as developed in the Cousot framework for abstract interpretation. The main difference between our approach and the standard theory of abstract interpretation is the choice of linear space structures instead of ordertheoretic ones as semantical (concrete and abstract) domains. We show that our method generates "best approximations" according to an appropriate notion of precision defined in terms of a norm. Moreover, if recasted in a ordertheoretic setting these approximations are correct in the sense of classical abstract interpretation theory. We use Concurrent ...
Labeled Markov processes: stronger and faster approximations
, 2004
"... This paper reports on and discusses three notions of approximation for Labelled Markov Processes that have been developed last year. The three schemes are improvements over former constructions [11,12] in the sense that they define approximants that capture more properties than before and that conve ..."
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Cited by 7 (3 self)
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This paper reports on and discusses three notions of approximation for Labelled Markov Processes that have been developed last year. The three schemes are improvements over former constructions [11,12] in the sense that they define approximants that capture more properties than before and that converge faster to the approximated process. One scheme is constructive and the two others are driven by properties on which one wants to focus. All three constructions involve quotienting the statespace in some way and the last two are quotients with respect to sets of temporal properties expressed in a simple logic with a greatest fixed point operator. This gives the possibility of customizing approximants with respect to properties of interest and is thus an important step towards using automated techniques intended for finite state systems, e.g., model checking, for continuous state systems. Another difference between the schemes is how they relate approximants with the approximated process. The requirement that approximants should be simulated by
Conditional Expectation and the Approximation of Labelled Markov Processes
 IN: CONCUR 2003  CONCURRENCY THEORY, LECTURE NOTES IN COMPUTER SCIENCE 2761 (2003
, 2003
"... We develop a new notion of approximation of labelled Markov processes based on the use of conditional expectations. The key idea is to approximate a system by a coarsegraining of the state space and using averages of the transition probabilities. This is unlike any of the previous notions based ..."
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Cited by 7 (4 self)
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We develop a new notion of approximation of labelled Markov processes based on the use of conditional expectations. The key idea is to approximate a system by a coarsegraining of the state space and using averages of the transition probabilities. This is unlike any of the previous notions based on the use of simulation. The resulting approximations are customizable, more accurate and stay within the world of LMPs. The use of averages and expectations may well also make the approximations more robust. We introduce a novel condition  called "granularity"  which leads to unique conditional expectations and which turns out to be a key concept despite its simplicity.
Approximation and Separability
"... F8.928> h1 Gg // G 2 0 h2 G 2 g // G 3 0 G 3 g // h3 ::: 1 F1 f F 2 1 Ff oo F 3 1 F 2 f oo ::: F 3 f oo (1) Here 0 is the initial metric space, 1 is the nal metric space, and, for all n < !, h n+1 := Fh n (G n+1 0 ,! FG n 0). Let G ! 0 be the colimit ..."
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F8.928> h1 Gg // G 2 0 h2 G 2 g // G 3 0 G 3 g // h3 ::: 1 F1 f F 2 1 Ff oo F 3 1 F 2 f oo ::: F 3 f oo (1) Here 0 is the initial metric space, 1 is the nal metric space, and, for all n < !, h n+1 := Fh n (G n+1 0 ,! FG n 0). Let G ! 0 be the colimit in Met of the !chain formed by the G n 0, with colimit injections n<F