On the Monte Carlo Boolean decision tree complexity of read-once formulae

In the Boolean decision tree model there is at least a linear gap between the Monte Carlo and the Las Vegas complexity of a function depending on the error probability. The author proves for a large class of read-once formulae that this trivial speed-up is the best that a Monte Carlo algorithm can achieve. For every formula F belonging to that class it is shown that the Monte Carlo complexity of F with two-sided error p is (1-2p)R(F), and with one-sided error p is (1-p)R(F), where R(F) denotes the Las Vegas complexity of F. The result follows from a general lower bound that is derived on the Monte Carlo complexity of these formulae.<<ETX>>

[1]  Ronald L. Rivest,et al.  On Recognizing Graph Properties from Adjacency Matrices , 1976, Theor. Comput. Sci..

[2]  Manuel Blum,et al.  Generic oracles and oracle classes , 1987, 28th Annual Symposium on Foundations of Computer Science (sfcs 1987).

[3]  Marc Snir,et al.  Lower Bounds on Probabilistic Linear Decision Trees , 1985, Theor. Comput. Sci..

[4]  Alan L. Selman.  One-Way Functions in Complexity Theory , 1990, MFCS.

[5]  Gábor Tardos,et al.  Query complexity, or why is it difficult to separateNPA∩coNPA fromPA by random oraclesA? , 1989, Comb..

[6]  Avi Wigderson,et al.  Randomized vs. deterministic decision tree complexity for read-once Boolean functions , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

[7]  Valerie King.  Lower bounds on the complexity of graph properties , 1988, STOC '88.

[8]  Péter Hajnal.  On the power of randomness in the decision tree model , 1990, Proceedings Fifth Annual Structure in Complexity Theory Conference.

[9]  Michael E. Saks,et al.  Probabilistic Boolean decision trees and the complexity of evaluating game trees , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[10]  Andrew Chi-Chih Yao.  Lower Bounds to Randomized Algorithms for Graph Properties , 1991, J. Comput. Syst. Sci..

[11]  Noam Nisan.  CREW PRAMs and Decision Trees , 1991, SIAM J. Comput..

[12]  Andrew Chi-Chih Yao,et al.  Probabilistic computations: Toward a unified measure of complexity , 1977, 18th Annual Symposium on Foundations of Computer Science (sfcs 1977).

[13]  Juris Hartmanis,et al.  One-Way Functions, Robustness, and the Non-Isomorphism of NP-Complete Sets , 1987, Proceeding Structure in Complexity Theory.

[14]  Avi Wigderson,et al.  On read-once threshold formulae and their randomized decision tree complexity , 1990, Proceedings Fifth Annual Structure in Complexity Theory Conference.