Improved bounds for the randomized decision tree Complexity of recursive majority

Random Structures and Algorithms

Volumn 48, Issue 3, 2016, Pages 612-638

  Magniez, Frédéric ^a   Nayak, Ashwin ^b   Santha, Miklos ^a,c   Sherman, Jonah ^d   Tardos, Gábor ^e   Xiao, David ^a  

^a CNRS   (France)

^b UNIVERSITY OF WATERLOO   (Canada)

^c NATIONAL UNIVERSITY OF SINGAPORE   (Singapore)

^d UNIVERSITY OF CALIFORNIA   (United States)

^e ALFRÉD RÉNYI INSTITUTE OF MATHEMATICS   (Hungary)

Author keywords

Randomized decision tree; Recursive majority

Indexed keywords

EID: 84961211021     PISSN: 10429832     EISSN: 10982418     Source Type: Journal    
DOI: 10.1002/rsa.20598     Document Type: Article

References (14)

1. M. Blum and R. Impagliazzo, General oracle and oracle classes, In Proceedings of 28th IEEE Symposium on Foundations of Computer Science, 1987, pp. 118-126.
2. J. Hartmanis and L. Hemachandra, One-way functions, robustness, and non-isomorphism of NP, -complete sets, In Proceedings of 2nd Structure in Complexity Theory Conference, 1987, pp. 160-173.
3. R. Heiman, I. Newman, and A. Wigderson, On read-once threshold formulae and their randomized decision tree complexity, In Proceedings of 5th Structure in Complexity Theory, 1990, pp. 78-87.
4. R. Heiman and A. Wigderson, Randomized versus deterministic decision tree complexity for read-once boolean functions, In Proceedings of 6th Structure in Complexity Theory Conference, 1991, pp. 172-179.
5. T. Jayram, R. Kumar, and D. Sivakumar, Two applications of information complexity, In Proceedings of 35th ACM Symposium on Theory of Computing, 2003, pp. 673-682.
6. I. Landau, A. Nachmias, Y. Peres, and S. Vanniasegaram, The lower bound for evaluating a recursive ternary majority function: an entropy-free proof, Technical report, Department of Statistics, University of California, Berkeley, CA Available at: https://www.stat.berkeley.edu/~vigre/undergrad/reports/parran, %20itamar%20vigre%20final%20report.pdf. Undergraduate Research Report.
7. N. Leonardos, An improved lower bound for the randomized decision tree complexity of recursive majority, In Fedor V. Fomin, Rusins Freivalds, Marta Z. Kwiatkowska, and David Peleg, editors, Proceedings of 40th International Colloquium on Automata, Languages and Programming, Volume of 7965 Lecture Notes in Computer Science, Springer, 2013, pp. 696-708.
8. F. Magniez, A. Nayak, M. Santha, and D. Xiao, Improved bounds for the randomized decision tree complexity of recursive majority, In Proceedings of 38th International Colloquium on Automata, Languages and Programming, 2011, pp. 317-329.
9. N. Nisan, CREW, PRAMs and decision trees, In Proceedings of 21st Annual ACM Symposium on Theory of Computing, 1989, pp. 327-335.
10. B. Reichardt and Spalek, Span-program-based quantum algorithm for evaluating formulas, In Proceedings of 40th ACM Symposium on Theory of Computing, 2008, pp. 103-112.
11. M. Saks and A. Wigderson, Probabilistic boolean decision trees and the complexity of evaluating game trees, Proceedings of 27th Annual Symposium on Foundations of Computer Science, 1986, pp. 29-38.
12. M. Santha, On the Monte Carlo, boolean decision tree complexity of read-once formulae, Random Struct Algorithms 6 (1995), 75-87.
13. M. Snir, Lower bounds for probabilistic linear decision trees, Theoret Comput Sci 38 (1995), 69-82.
14. G. Tardos, Query complexity or why is it difficult to separate NPA∩coNPA from PA by a random oracle, Combinatorica 9 (1990), 385-392.