The complexity of probabilistic verification
Journal of the ACM (JACM)
Modeling and analysis of stochastic systems
Modeling and analysis of stochastic systems
Some Recursive Unsolvable Problems Relating to Isolated Cutpoints in Probabilistic Automata
Proceedings of the Fourth Colloquium on Automata, Languages and Programming
Recognizing ?-regular Languages with Probabilistic Automata
LICS '05 Proceedings of the 20th Annual IEEE Symposium on Logic in Computer Science
Introduction to probabilistic automata (Computer science and applied mathematics)
Introduction to probabilistic automata (Computer science and applied mathematics)
Lower bounds for natural proof systems
SFCS '77 Proceedings of the 18th 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
Relationships between nondeterministic and deterministic tape complexities
Journal of Computer and System Sciences
On decision problems for probabilistic Büchi automata
FOSSACS'08/ETAPS'08 Proceedings of the Theory and practice of software, 11th international conference on Foundations of software science and computational structures
Probabilistic automata on finite words: decidable and undecidable problems
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming: Part II
Finitary winning in ω-regular games
TACAS'06 Proceedings of the 12th international conference on Tools and Algorithms for the Construction and Analysis of Systems
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A Finite Probabilistic Table, or FPT, consists of a finite state space S, an initial distribution on S, and a finite set of Markov matrices on S, labeled by an alphabet @S. An infinite word on @S induces a non-homogeneous Markov chain (NHMC) on S. In the context of finite homogeneous Markov chains, a state s is recurrent if with probability one a run initialized on s visits s infinitely often. Equivalently, s is recurrent if with probability one, the proportion of time a run initialized on s spends on s converges to a non-zero limit. In this paper we introduce two natural notions of recurrence for non-homogeneous Markovian processes: a state s is weakly recurrent (resp. strongly recurrent) if with positive probability the process visits s infinitely often (resp. spends a non-zero proportion of time on s). These notions do not coincide in the context of NHMCs, and we study the related computational problem on FPTs: given an FPT and a state s, is there w@?@S^~ such that s is weakly (resp. strongly) recurrent for the associated NHMC? We prove that the strong recurrence problem is PSPACE-complete, along with other complexity results, which contrast with previous results which showed for instance the undecidability of the weak recurrence problem.