Exact lower time bounds for computing Boolean functions on CREW PRAMs
Journal of Computer and System Sciences
Bounds for Small-Error and Zero-Error Quantum Algorithms
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Every decision tree has an in.uential variable
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
Span-program-based quantum algorithm for evaluating formulas
STOC '08 Proceedings of the fortieth annual ACM symposium on Theory of computing
Lower bounds to randomized algorithms for graph properties
SFCS '87 Proceedings of the 28th Annual Symposium on Foundations of Computer Science
A randomized competitive algorithm for evaluating priced AND/OR trees
Theoretical Computer Science
The Complexity of Algorithms Computing Game Trees on Random Assignments
AAIM '07 Proceedings of the 3rd international conference on Algorithmic Aspects in Information and Management
Quantum Algorithms for Evaluating Min-Max Trees
Theory of Quantum Computation, Communication, and Cryptography
Finding optimal satisficing strategies for and-or trees
Artificial Intelligence
The computational complexity of game trees by eigen-distribution
COCOA'07 Proceedings of the 1st international conference on Combinatorial optimization and applications
On directional vs. undirectional randomized decision tree complexity for read-once formulas
CATS '10 Proceedings of the Sixteenth Symposium on Computing: the Australasian Theory - Volume 109
Algorithms and theory of computation handbook
New developments in quantum algorithms
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Depth-independent lower bounds on the communication complexity of read-once Boolean formulas
COCOON'10 Proceedings of the 16th annual international conference on Computing and combinatorics
Any AND-OR Formula of Size $N$ Can Be Evaluated in Time $N^{1/2+o(1)}$ on a Quantum Computer
SIAM Journal on Computing
On the competitive ratio of evaluating priced functions
Journal of the ACM (JACM)
Competitive Boolean function evaluation: Beyond monotonicity, and the symmetric case
Discrete Applied Mathematics
The quantum query complexity of certification
Quantum Information & Computation
Improved bounds for the randomized decision tree complexity of recursive majority
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Super-polynomial quantum speed-ups for boolean evaluation trees with hidden structure
Proceedings of the 3rd Innovations in Theoretical Computer Science Conference
All quantum adversary methods are equivalent
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Reflections for quantum query algorithms
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Bounding the randomized decision tree complexity of read-once Boolean functions
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
Algorithmics in exponential time
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
A stronger LP bound for formula size lower bounds via clique constraints
Theoretical Computer Science
Quantum adversary (upper) bound
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
On the possibilities and limitations of pseudodeterministic algorithms
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Evasiveness through a circuit lens
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
Properties and applications of boolean function composition
Proceedings of the 4th conference on Innovations in Theoretical Computer Science
On the complexity of trial and error
Proceedings of the forty-fifth annual ACM symposium on Theory of computing
An improved lower bound for the randomized decision tree complexity of recursive majority,
ICALP'13 Proceedings of the 40th international conference on Automata, Languages, and Programming - Volume Part I
Gems in decision tree complexity revisited
ACM SIGACT News
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The Boolean Decision tree model is perhaps the simplest model that computes Boolean functions; it charges only for reading an input variable. We study the power of randomness (vs. both determinism and non-determinism) in this model, and prove separation results between the three complexity measures. These results are obtained via general and efficient methods for computing upper and lower bounds on the probabilistic complexity of evaluating Boolean formulae in which every variable appears exactly once (AND/OR tree with distinct leaves). These bounds are shown to be exactly tight for interesting families of such tree functions. We then apply our results to the complexity of evaluating game trees, which is a central problem in AI. These trees are similar to Boolean tree functions, except that input variables (leaves) may take values from a large set (of valuations to game positions) and the AND/OR nodes are replaced by MIN/MAX nodes. Here the cost is the number of positions (leaves) probed by the algorithm. The best known algorithm for this problem is the alpha-beta pruning method. As a deterministic algorithm, it will in the worst case have to examine all positions. Many papers studied the expected behavior of alpha-beta pruning (on uniform trees) under the unreasonable assumption that position values are drawn independently from some distribution. We analyze a randomized variant of alphabeta pruning, show that it is considerably faster than the deterministic one in worst case, and prove it optimal for uniform trees.