Verification of multiprocess probabilistic protocols
Distributed Computing
Algorithms for computer algebra
Algorithms for computer algebra
Crowds: anonymity for Web transactions
ACM Transactions on Information and System Security (TISSEC)
Model Checking of Probabalistic and Nondeterministic Systems
Proceedings of the 15th Conference on Foundations of Software Technology and Theoretical Computer Science
Weak Bisimulation for Fully Probabilistic Processes
CAV '97 Proceedings of the 9th International Conference on Computer Aided Verification
Optimal state-space lumping in Markov chains
Information Processing Letters
ProbMela and verification of Markov decision processes
ACM SIGMETRICS Performance Evaluation Review
Parametric probabilistic transition systems for system design and analysis
Formal Aspects of Computing
Symbolic Partition Refinement with Dynamic Balancing of Time and Space
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
Regular Expressions for PCTL Counterexamples
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
Approximate Parameter Synthesis for Probabilistic Time-Bounded Reachability
RTSS '08 Proceedings of the 2008 Real-Time Systems Symposium
Comparative branching-time semantics for Markov chains
Information and Computation
SFM'07 Proceedings of the 7th international conference on Formal methods for performance evaluation
Optimal lower bounds on regular expression size using communication complexity
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Symbolic and parametric model checking of discrete-time markov chains
ICTAC'04 Proceedings of the First international conference on Theoretical Aspects of Computing
ICMS'06 Proceedings of the Second international conference on Mathematical Software
Model-Checking markov chains in the presence of uncertainties
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
PRISM: a tool for automatic verification of probabilistic systems
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Run-time efficient probabilistic model checking
Proceedings of the 33rd International Conference on Software Engineering
A compositional method for reliability analysis of workflows affected by multiple failure modes
Proceedings of the 14th international ACM Sigsoft symposium on Component based software engineering
QoS verification and model tuning @ runtime
Proceedings of the 19th ACM SIGSOFT symposium and the 13th European conference on Foundations of software engineering
PARAM: a model checker for parametric markov models
CAV'10 Proceedings of the 22nd international conference on Computer Aided Verification
ASE '11 Proceedings of the 2011 26th IEEE/ACM International Conference on Automated Software Engineering
Evolution, adaptation, and the quest for incrementality
Proceedings of the 17th Monterey conference on Large-Scale Complex IT Systems: development, operation and management
Probabilistic model checking of the PDGF signaling pathway
Transactions on Computational Systems Biology XIV
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Given a parametric Markov model, we consider the problem of computing the rational function expressing the probability of reaching a given set of states. To attack this principal problem, Daws has suggested to first convert the Markov chain into a finite automaton, from which a regular expression is computed. Afterwards, this expression is evaluated to a closed form function representing the reachability probability. This paper investigates how this idea can be turned into an effective procedure. It turns out that the bottleneck lies in the growth of the regular expression relative to the number of states (n *** (logn )). We therefore proceed differently, by tightly intertwining the regular expression computation with its evaluation. This allows us to arrive at an effective method that avoids this blow up in most practical cases. We give a detailed account of the approach, also extending to parametric models with rewards and with non-determinism. Experimental evidence is provided, illustrating that our implementation provides meaningful insights on non-trivial models.