On P versus NP∩CO-NP for decision trees and read-once branching programs

Computational Complexity

Volumn 8, Issue 4, 1999, Pages 357-370

  Jukna, S ^a,b   Razborov, A ^d   Savicky P ^c   Wegener, I ^e  

^a UNIVERSITY OF TRIER   (Germany)

^b Institute of Mathematics   (Lithuania)

^c INSTITUTE OF COMPUTER SCIENCE   (Czech Republic)

^d STEKLOV MATHEMATICAL INSTITUTE   (Russian Federation)

^e TU DORTMUND UNIVERSITY   (Germany)

Author keywords

Boolean functions; Branching programs; Computational complexity; Decision trees; P versus NP co NP

Indexed keywords

EID: 0033258962     PISSN: 10163328     EISSN: None     Source Type: Journal    
DOI: 10.1007/s000370050005     Document Type: Article

References (19)

1. F. ABLAYEV. Randomization and nondeterminism are incomparable for polynomial ordered binary decision diagrams. In Proc. ICALP '97, Lecture Notes in Comput. Sci. 1256, Springer, Berlin, 1997, 195-202.
2. 1-formulae on unite structures. Ann. Pure Applied Logic 24 (1983), 1-48.
3. A. BLOKHUIS. On the size of a blocking set in PG(2,p). Combinatorica 14 (1994), 111-114.
4. M. BLUM AND R. IMPAGLIAZZO. Generic oracles and oracle classes. In Proc. 28th IEEE FOCS, 1987, 118-126.
5. A. A. BRUEN. Baer subplanes and blocking sets. Bull. Amer. Math. Soc. 76 (1970), 342-344.
6. A. EHRENFEUCHT AND D. HAUSSLER. Learning decision trees from random examples. Inform. and Comput. 82 (1989), 231-246.
7. M. FÜRST, J. SAXE AND M. SIPSER. Parity, circuits and the polynomial time hierarchy. In Proc. 22nd IEEE FOCS, 1981, 260-270.
8. A. GÁL. A simple function that requires exponential size read-once branching programs. Inform. Process. Letters 62 (1997), 13-16.
9. J. HARTMANIS AND L. A. HEMACHANDRA. One-way functions, robustness and non-isomorphism of NP-complete classes. Tech. Rep. DCS TR86-796, Cornell University, 1987.
10. J. HÅSTAD. Almost optimal lower bounds for small depth circuits. In S. Micali, editor, Randomness and Computation (Advances in Computing Research, Vol. 5), JAI Press, 1989, 143-170.
11. S. JUKNA. Entropy of contact circuits and lower bounds on their complexity. Theoret. Comput. Sci. 57 (1988), 113-129.
12. E. KUSHILEVITZ AND Y. MANSOUR. Learning decision trees using the Fourier spectrum. In Proc. 23rd ACM STOC, 1991, 455-464.
13. N. LINIAL, Y. MANSOUR AND N. NISAN. Constant depth circuits, Fourier transforms and learnability. In Proc. 30th IEEE FOCS, 1989, 574-579.
14. A. A. RAZBOROV. Lower bounds for deterministic and nondeterministic branching programs. In Proc. FCT'91, Lecture Notes in Comput. Sci. 529, Springer, Berlin, 1991, 47-60.
15. M. SAKS AND A. WIGDERSON. Probabilistic Boolean decision trees and the complexity of evaluating games. In Proc. 27th IEEE FOCS, 1986, 29-38.
16. P. SAVICKÝ AND S. ŽÁK. A large lower bound for 1-branching programs, TR96-036, ECCC, Trier, 1996.
17. A by a random oracle A? Combinatorica 9 (1989), 385-392.
18. I. WEGENER. The Complexity of Boolean Functions. Wiley-Teubner, 1987.
19. A. YAO. Separating the polynomial-time hierarchy by oracles. In Proc. 26th IEEE FOCS, 1985, 1-10.