Competitive Markov decision processes
Competitive Markov decision processes
Journal of the ACM (JACM)
Deterministic one-counter automata
1. Fachtagung über Automatentheorie und Formale Sprachen
The complexity of bisimilarity-checking for one-counter processes
Theoretical Computer Science
DP Lower bounds for equivalence-checking and model-checking of one-counter automata
Information and Computation
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Numerical Methods for Structured Markov Chains (Numerical Mathematics and Scientific Computation)
Quasi-Birth-Death Processes, Tree-Like QBDs, Probabilistic 1-Counter Automata, and Pushdown Systems
QEST '08 Proceedings of the 2008 Fifth International Conference on Quantitative Evaluation of Systems
A Computational Introduction to Number Theory and Algebra
A Computational Introduction to Number Theory and Algebra
Pure stationary optimal strategies in Markov decision processes
STACS'07 Proceedings of the 24th annual conference on Theoretical aspects of computer science
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Parity games played on transition graphs of one-counter processes
FOSSACS'06 Proceedings of the 9th European joint conference on Foundations of Software Science and Computation Structures
Recursive markov decision processes and recursive stochastic games
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Reachability in recursive markov decision processes
CONCUR'06 Proceedings of the 17th international conference on Concurrency Theory
Bisimilarity of one-counter processes is PSPACE-complete
CONCUR'10 Proceedings of the 21st international conference on Concurrency theory
Runtime analysis of probabilistic programs with unbounded recursion
ICALP'11 Proceedings of the 38th international conference on Automata, languages and programming - Volume Part II
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
Efficient analysis of probabilistic programs with an unbounded counter
CAV'11 Proceedings of the 23rd international conference on Computer aided verification
Energy and mean-payoff parity markov decision processes
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Games and markov decision processes with mean-payoff parity and energy parity objectives
MEMICS'11 Proceedings of the 7th international conference on Mathematical and Engineering Methods in Computer Science
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
Determinacy and optimal strategies in infinite-state stochastic reachability games
Theoretical Computer Science
Branching-time model-checking of probabilistic pushdown automata
Journal of Computer and System Sciences
Bisimulation equivalence and regularity for real-time one-counter automata
Journal of Computer and System Sciences
Analyzing probabilistic pushdown automata
Formal Methods in System Design
Hi-index | 0.00 |
We study the computational complexity of some central analysis problems for One-Counter Markov Decision Processes (OC-MDPs), a class of finitely-presented, countable-state MDPs. OC-MDPs extend finite-state MDPs with an unbounded counter. The counter can be incremented, decremented, or not changed during each state transition, and transitions may be enabled or not depending on both the current state and on whether the counter value is 0 or not. Some states are "random", from where the next transition is chosen according to a given probability distribution, while other states are "controlled", from where the next transition is chosen by the controller. Different objectives for the controller give rise to different computational problems, aimed at computing optimal achievable objective values and optimal strategies. OC-MDPs are in fact equivalent to a controlled extension of (discrete-time) Quasi-Birth-Death processes (QBDs), a purely stochastic model heavily studied in queueing theory and applied probability. They can thus be viewed as a natural "adversarial" extension of a classic stochastic model. They can also be viewed as a natural probabilistic/controlled extension of classic one-counter automata. OC-MDPs also subsume (as a very restricted special case) a recently studied MDP model called "solvency games" that model a risk-averse gambling scenario. Basic computational questions for OC-MDPs include "termination" questions and "limit" questions, such as the following: does the controller have a strategy to ensure that the counter (which may, for example, count the number of jobs in the queue) will hit value 0 (the empty queue) almost surely (a.s.)? Or that the counter will have lim sup value ∞, a.s.? Or, that it will hit value 0 in a selected terminal state, a.s.? Or, in case such properties are not satisfied almost surely, compute their optimal probability over all strategies. We provide new upper and lower bounds on the complexity of such problems. Specifically, we show that several quantitative and almost-sure limit problems can be answered in polynomial time, and that almost-sure termination problems (without selection of desired terminal states) can also be answered in polynomial time. On the other hand, we show that the almost-sure termination problem with selected terminal states is PSPACE-hard and we provide an exponential time algorithm for this problem. We also characterize classes of strategies that suffice for optimality in several of these settings. Our upper bounds combine a number of techniques from the theory of MDP reward models, the theory of random walks, and a variety of automata-theoretic methods.