The complexity of probabilistic verification
Journal of the ACM (JACM)
On Communicating Finite-State Machines
Journal of the ACM (JACM)
Measure and probability for concurrency theorists
Theoretical Computer Science - Special issues on models and paradigms for concurrency
Automatic verification of real-time systems with discrete probability distributions
Theoretical Computer Science
Model-Checking for Probabilistic Real-Time Systems (Extended Abstract)
ICALP '91 Proceedings of the 18th International Colloquium on Automata, Languages and Programming
Model Checking Probabilistic Pushdown Automata
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
PRISM 2.0: A Tool for Probabilistic Model Checking
QEST '04 Proceedings of the The Quantitative Evaluation of Systems, First International Conference
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
Automatic verification of probabilistic concurrent finite state programs
SFCS '85 Proceedings of the 26th Annual Symposium on Foundations of Computer Science
Verification of probabilistic systems with faulty communication
Information and Computation
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
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
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
FORTE'06 Proceedings of the 26th IFIP WG 6.1 international conference on Formal Techniques for Networked and Distributed Systems
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
Computable fixpoints in well-structured symbolic model checking
Formal Methods in System Design
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In the past 5 years, a series of verification algorithms has been proposed for infinite Markov chains that have a finite attractor, i.e., a set that will be visited infinitely often almost surely starting from any state. In this paper, we establish a sufficient criterion for the existence of an attractor. We show that if the states of a Markov chain can be given levels (positive integers) such that the expected next level for states at some level n0 is less than n-@D for some positive @D, then the states at level 0 constitute an attractor for the chain. As an application, we obtain a direct proof that some probabilistic channel systems combining message losses with duplication and insertion errors have a finite attractor.