The complexity of probabilistic verification
Journal of the ACM (JACM)
Model checking
Model-checking continuous-time Markov chains
ACM Transactions on Computational Logic (TOCL)
Algorithmic analysis of programs with well quasi-ordered domains
Information and Computation - Special issue: LICS 1996—Part 1
Symbolic Model Checking of Probabilistic Processes Using MTBDDs and the Kronecker Representation
TACAS '00 Proceedings of the 6th International Conference on Tools and Algorithms for Construction and Analysis of Systems: Held as Part of the European Joint Conferences on the Theory and Practice of Software, ETAPS 2000
Probabilistic Lossy Channel Systems
TAPSOFT '97 Proceedings of the 7th International Joint Conference CAAP/FASE on Theory and Practice of Software Development
Reasoning about Probabilistic Lossy Channel Systems
CONCUR '00 Proceedings of the 11th International Conference on Concurrency Theory
Automated Performance and Dependability Evaluation Using Model Checking
Performance Evaluation of Complex Systems: Techniques and Tools, Performance 2002, Tutorial Lectures
Establishing Qualitative Properties for Probabilistic Lossy Channel Systems: An Algorithmic Approach
ARTS '99 Proceedings of the 5th International AMAST Workshop on Formal Methods for Real-Time and Probabilistic Systems
Probabilistic temporal logics for finite and bounded models
STOC '84 Proceedings of the sixteenth annual ACM symposium on Theory of computing
Model Checking Probabilistic Pushdown Automata
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Model checking meets performance evaluation
ACM SIGMETRICS Performance Evaluation Review
Probabilistic model checking in practice: case studies with PRISM
ACM SIGMETRICS Performance Evaluation Review
Quantitative Analysis of Probabilistic Pushdown Automata: Expectations and Variances
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Verifying Infinite Markov Chains with a Finite Attractor or the Global Coarseness Property
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Limiting Behavior of Markov Chains with Eager Attractors
QEST '06 Proceedings of the 3rd international conference on the Quantitative Evaluation of Systems
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
A note on the attractor-property of infinite-state Markov chains
Information Processing Letters
Verification of probabilistic systems with faulty communication
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
Model checking lossy channels systems is probably decidable
FOSSACS'03/ETAPS'03 Proceedings of the 6th International conference on Foundations of Software Science and Computation Structures and joint European conference on Theory and practice of software
Quantitative analysis of probabilistic lossy channel systems
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
Recursive markov decision processes and recursive stochastic games
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Computing the expected accumulated reward and gain for a subclass of infinite markov chains
FSTTCS '05 Proceedings of the 25th international conference on Foundations of Software Technology and Theoretical Computer Science
Recursive markov chains, stochastic grammars, and monotone systems of nonlinear equations
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
Algorithmic verification of recursive probabilistic state machines
TACAS'05 Proceedings of the 11th international conference on Tools and Algorithms for the Construction and Analysis of Systems
Verifying probabilistic procedural programs
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
Stochastic games with lossy channels
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Carrying probabilities to the infinite world
CONCUR'11 Proceedings of the 22nd international conference on Concurrency theory
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We consider infinite-state discrete Markov chains which are eager: the probability of avoiding a defined set of final states for more than n steps is bounded by some exponentially decreasing function f(n). We prove that eager Markov chains include those induced by Probabilistic Lossy Channel Systems, Probabilistic Vector Addition Systems with States, and Noisy Turing Machines, and that the bounding function f(n) can be effectively constructed for them. Furthermore, we study the problem of computing the expected reward (or cost) of runs until reaching the final states, where rewards are assigned to individual runs by computable reward functions. For eager Markov chains, an effective path exploration scheme, based on forward reachability analysis, can be used to approximate the expected reward up-to an arbitrarily small error.