Matrix analysis
The complexity of stochastic games
Information and Computation
Competitive Markov decision processes
Competitive Markov decision processes
Foundations of statistical natural language processing
Foundations of statistical natural language processing
Some NP-complete geometric problems
STOC '76 Proceedings of the eighth 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
Analysis of recursive state machines
ACM Transactions on Programming Languages and Systems (TOPLAS)
Recursive markov decision processes and recursive stochastic games
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
On the decidability of temporal properties of probabilistic pushdown automata
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of 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
Reachability in recursive Markov decision processes
Information and Computation
Automata, Probability, and Recursion
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
Recursive Markov chains, stochastic grammars, and monotone systems of nonlinear equations
Journal of the ACM (JACM)
Regularity in PDA Games Revisited
Electronic Notes in Theoretical Computer Science (ENTCS)
Computational Aspects of Equilibria
SAGT '09 Proceedings of the 2nd International Symposium on Algorithmic Game Theory
PReMo: an analyzer for probabilistic recursive models
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
One-counter Markov decision processes
SODA '10 Proceedings of the twenty-first annual ACM-SIAM symposium on Discrete Algorithms
Qualitative reachability in stochastic BPA games
Information and Computation
Approximating the termination value of one-counter MDPS and stochastic games
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
Recursive concurrent stochastic games
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part II
Reachability in recursive markov decision processes
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
Analysis of recursive probabilistic models
ATVA'06 Proceedings of the 4th international conference on Automated Technology for Verification and Analysis
Minimizing expected termination time in one-counter markov decision processes
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part II
Playing games with counter automata
RP'12 Proceedings of the 6th international conference on Reachability Problems
Approximating the termination value of one-counter MDPs and stochastic games
Information and Computation
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Recursive Markov Decision Processes (RMDPs) and Recursive Simple Stochastic Games (RSSGs) are natural models for recursive systems involving both probabilistic and non-probabilistic actions. As shown recently [10], fundamental problems about such models, e.g., termination, are undecidable in general, but decidable for the important class of 1-exit RMDPs and RSSGs. These capture controlled and game versions of multi-type Branching Processes, an important and well-studied class of stochastic processes. In this paper we provide efficient algorithms for the qualitative termination problem for these models: does the process terminate almost surely when the players use their optimal strategies? Polynomial time algorithms are given for both maximizing and minimizing 1-exit RMDPs (the two cases are not symmetric). For 1-exit RSSGs the problem is in NP∩coNP, and furthermore, it is at least as hard as other well-known NP∩coNP problems on games, e.g., Condon's quantitative termination problem for finite SSGs ([3]). For the class of linearly-recursive 1-exit RSSGs, we show that the problem can be solved in polynomial time.