The complexity of Markov decision processes
Mathematics of Operations Research
A model for reasoning about persistence and causation
Computational Intelligence
A catalog of complexity classes
Handbook of theoretical computer science (vol. A)
The complexity of finite functions
Handbook of theoretical computer science (vol. A)
Abstraction and approximate decision-theoretic planning
Artificial Intelligence
AAAI '99/IAAI '99 Proceedings of the sixteenth national conference on Artificial intelligence and the eleventh Innovative applications of artificial intelligence conference innovative applications of artificial intelligence
Complexity of finite-horizon Markov decision process problems
Journal of the ACM (JACM)
Proof-complexity results for nonmonotonic reasoning
ACM Transactions on Computational Logic (TOCL)
Monotonic reductions, representative equivalence, and compilation of intractable problems
Journal of the ACM (JACM)
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computing Factored Value Functions for Policies in Structured MDPs
IJCAI '99 Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence
Preprocessing of intractable problems
Information and Computation
The size of MDP factored policies
Eighteenth national conference on Artificial intelligence
Some connections between nonuniform and uniform complexity classes
STOC '80 Proceedings of the twelfth annual ACM symposium on Theory of computing
Dynamic Programming
Speeding up the convergence of value iteration in partially observable Markov decision processes
Journal of Artificial Intelligence Research
The computational complexity of probabilistic planning
Journal of Artificial Intelligence Research
Probabilistic propositional planning: representations and complexity
AAAI'97/IAAI'97 Proceedings of the fourteenth national conference on artificial intelligence and ninth conference on Innovative applications of artificial intelligence
On the complexity of solving Markov decision problems
UAI'95 Proceedings of the Eleventh conference on Uncertainty in artificial intelligence
Incremental pruning: a simple, fast, exact method for partially observable Markov decision processes
UAI'97 Proceedings of the Thirteenth conference on Uncertainty in artificial intelligence
A bounded statistical approach for model checking of unbounded until properties
Proceedings of the IEEE/ACM international conference on Automated software engineering
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Policies of Markov Decision Processes (MDPs) determine the next action to execute from the current state and, possibly, the history (the past states). When the number of states is large, succinct representations are often used to compactly represent both the MDPs and the policies in a reduced amount of space. In this paper, some problems related to the size of succinctly represented policies are analyzed. Namely, it is shown that some MDPs have policies that can only be represented in space super-polynomial in the size of the MDP, unless the polynomial hierarchy collapses. This fact motivates the study of the problem of deciding whether a given MDP has a policy of a given size and reward. Since some algorithms for MDPs work by finding a succinct representation of the value function, the problem of deciding the existence of a succinct representation of a value function of a given size and reward is also considered.