Probabilistic verification and approximation

We study the existence of efficient approximation methods to verify quantitative specifications of probabilistic systems. Models of such systems are labelled discrete time Markov chains and checking specifications consists of computing satisfaction probabilities of linear temporal logic formulas. We...

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Bibliographic Details
Published in:	Annals of pure and applied logic Vol. 152; no. 1; pp. 122 - 131
Main Authors:	Lassaigne, Richard, Peyronnet, Sylvain
Format:	Journal Article
Language:	English
Published:	Elsevier B.V 01.03.2008
Subjects:	Probabilistic verification Randomized approximation algorithms 68W20 Probabilistic verification Randomized approximation algorithms 68Q60
ISSN:	0168-0072
Online Access:	Get full text
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Summary:	We study the existence of efficient approximation methods to verify quantitative specifications of probabilistic systems. Models of such systems are labelled discrete time Markov chains and checking specifications consists of computing satisfaction probabilities of linear temporal logic formulas. We prove that, in general, there is no polynomial time randomized approximation scheme with relative error for probabilistic verification. However, in many applications, specifications can be expressed by monotone formulas or negation of monotone formulas and randomized approximation schemes with absolute error are sufficient. We show how some simple randomized approximation algorithms can improve the efficiency of verification of such probabilistic specifications and can be implemented in a probabilistic model checker.
ISSN:	0168-0072
DOI:	10.1016/j.apal.2007.11.006