On the power of randomness in the decision tree model

Results suggest that there are relations between the decision tree complexity of a Boolean function and its symmetry. A central conjecture is that for any monotone graph property the randomized decision tree complexity does not differ from the deterministic one with more than a constant factor. The...

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Bibliographic Details
Published inProceedings Fifth Annual Structure in Complexity Theory Conference pp. 66 - 77
Main Author Hajnal, P.
Format Conference Proceeding
LanguageEnglish
Published IEEE Comput. Soc. Press 1990
Subjects
Bipartite graph
Boolean functions
Complexity theory
Computational modeling
Computer science
Concurrent computing
Decision trees
Heart
Positron emission tomography
Probability distribution
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Summary:Results suggest that there are relations between the decision tree complexity of a Boolean function and its symmetry. A central conjecture is that for any monotone graph property the randomized decision tree complexity does not differ from the deterministic one with more than a constant factor. The authors improve on V. King's Omega (n/sup 5/4/) lower bound on the randomized decision tree complexity of monotone graph properties to Omega (n/sup 4/3/). The proof follows A. Yao's (1977) approach and improves it in a different direction from King's. At the heart of the proof is a duality argument combined with a new packing lemma for bipartite graphs. Consideration is also given to the question of what distinguishes graph properties from other highly symmetric Boolean functions, where randomization can help significantly. Open questions concerning this problem are discussed.< >
ISBN:0818660724
9780818660726
DOI:10.1109/SCT.1990.113955