Graph-Based Algorithms for Boolean Function Manipulation
IEEE Transactions on Computers
Foundations of logic programming; (2nd extended ed.)
Foundations of logic programming; (2nd extended ed.)
Algebraic decision diagrams and their applications
ICCAD '93 Proceedings of the 1993 IEEE/ACM international conference on Computer-aided design
Stochastic dynamic programming with factored representations
Artificial Intelligence
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Markov Decision Processes: Discrete Stochastic Dynamic Programming
Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Introduction to Statistical Relational Learning (Adaptive Computation and Machine Learning)
Introduction to Statistical Relational Learning (Adaptive Computation and Machine Learning)
Exploiting shared correlations in probabilistic databases
Proceedings of the VLDB Endowment
Practical solution techniques for first-order MDPs
Artificial Intelligence
Lifted probabilistic inference with counting formulas
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 2
Lifted first-order belief propagation
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 2
Efficient solution algorithms for factored MDPs
Journal of Artificial Intelligence Research
FLUCAP: a heuristic search planner for first-order MDPs
Journal of Artificial Intelligence Research
First order decision diagrams for relational MDPs
Journal of Artificial Intelligence Research
Efficient reinforcement learning in factored MDPs
IJCAI'99 Proceedings of the 16th international joint conference on Artificial intelligence - Volume 2
First-order probabilistic inference
IJCAI'03 Proceedings of the 18th international joint conference on Artificial intelligence
Symbolic dynamic programming for first-order MDPs
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Lifted first-order probabilistic inference
IJCAI'05 Proceedings of the 19th international joint conference on Artificial intelligence
Lifted aggregation in directed first-order probabilistic models
IJCAI'09 Proceedings of the 21st international jont conference on Artifical intelligence
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Bisimulation-based approximate lifted inference
UAI '09 Proceedings of the Twenty-Fifth Conference on Uncertainty in Artificial Intelligence
Probabilistic relational planning with first order decision diagrams
Journal of Artificial Intelligence Research
SPUDD: stochastic planning using decision diagrams
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
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Many tasks in AI require representation and manipulation of complex functions. First-Order Decision Diagrams (FODD) are a compact knowledge representation expressing functions over relational structures. They represent numerical functions that, when constrained to the Boolean range, use only existential quantification. Previous work has developed a set of operations for composition and for removing redundancies in FODDs, thus keeping them compact, and showed how to successfully employ FODDs for solving large-scale stochastic planning problems through the formalism of relational Markov decision processes (RMDP). In this paper, we introduce several new ideas enhancing the applicability of FODDs. More specifically, we first introduce Generalized FODDs (GFODD) and composition operations for them, generalizing FODDs to arbitrary quantification. Second, we develop a novel approach for reducing (G)FODDs using model checking. This yields - for the first time - a reduction that maximally reduces the diagram for the FODD case and provides a sound reduction procedure for GFODDs. Finally we show how GFODDs can be used in principle to solve RMDPs with arbitrary quantification, and develop a complete solution for the case where the reward function is specified using an arbitrary number of existential quantifiers followed by an arbitrary number of universal quantifiers.