The complexity of propositional linear temporal logics
Journal of the ACM (JACM)
Automatic verification of finite-state concurrent systems using temporal logic specifications
ACM Transactions on Programming Languages and Systems (TOPLAS)
Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Monte-Carlo approximation algorithms for enumeration problems
Journal of Algorithms
SIAM Journal on Computing
The complexity of probabilistic verification
Journal of the ACM (JACM)
Checking that finite state concurrent programs satisfy their linear specification
POPL '85 Proceedings of the 12th ACM SIGACT-SIGPLAN symposium on Principles of programming languages
SIAM Journal on Computing
An Optimal Algorithm for Monte Carlo Estimation
SIAM Journal on Computing
Approximate Verification of Probabilistic Systems
PAPM-PROBMIV '02 Proceedings of the Second Joint International Workshop on Process Algebra and Probabilistic Methods, Performance Modeling and Verification
Model Checking of Probabalistic and Nondeterministic Systems
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
Probabilistic Verification of Discrete Event Systems Using Acceptance Sampling
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
Monte-Carlo algorithms for enumeration and reliability problems
SFCS '83 Proceedings of the 24th Annual Symposium on Foundations of Computer Science
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Probabilistic Model Checking of the CSMA/CD Protocol Using PRISM and APMC
Electronic Notes in Theoretical Computer Science (ENTCS)
Evaluating Complex MAC Protocols for Sensor Networks with APMC
Electronic Notes in Theoretical Computer Science (ENTCS)
Automated reliability estimation over partial systematic explorations
Proceedings of the 2013 International Conference on Software Engineering
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Model checking is an algorithmic method allowing to automatically verify if a system which is represented as a Kripke model satisfies a given specification. Specifications are usually expressed by formulas of temporal logic. The first objective of this paper is to give an overview of methods able to verify probabilistic systems. Models of such systems are labelled discrete time Markov chains and specifications are expressed in extensions of temporal logic by probabilistic operators. The second objective is to focus on the complexity of these methods and to answer the question: can probabilistic verification be efficiently approximated? In general, the answer is negative. However, in many applications, the specification formulas can be expressed in some positive fragment of linear time temporal logic. In this paper, we show how some simple randomized approximation algorithms can improve the efficiency of the verification of such probabilistic specifications.