Small pseudo-random sets yield hard functions: New tight explicit lower bounds for branching programs (extended abstract)

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1644 LNCS, Issue , 1999, Pages 179-189

  Andreev, Alexander E ^a   Baskakov, Juri L ^b   Clementi, Andrea E F ^c   Rolim, José D P ^d  

^a AGERE SYSTEMS   (United States)

^b MOSCOW STATE UNIVERSITY   (Russian Federation)

^c UNIVERSITY OF ROME TOR VERGATA   (Italy)

^d UNIVERSITY OF GENEVA   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

AUTOMATA THEORY; SET THEORY;

BRANCHING PROGRAMS; CARDINALITIES; EXPLICIT CONSTRUCTIONS; EXTENDED ABSTRACTS; HARD FUNCTION; LOWER BOUNDS; PSEUDO RANDOM; SAMPLE SPACE;

BOOLEAN FUNCTIONS;

EID: 84887413327     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-48523-6_15     Document Type: Conference Paper

References (23)

1. N. Alon, O. Goldreich, J. Hastad, and R. Peralta (1990), Simple Constructions of Almost k-wise Independent Random Variables", Proc. of IEEE-FOCS, Vol. 2, pp. 544-553.
2. A. Andreev, A. Clementi, and J. Rolim (1997), Worst-case Hardness Sufices for Derandomization: A New method for Hardness-Randomness Trade-Offs", in Proc. of ICALP, LNCS, 1256, pp. 177-187 (to appear also on TCS).
3. A. Andreev, A. Clementi, J. Rolim (1997), Eficient Constructions of Hitting Sets for Systems of Linear Functions", in ECCC TR96-029, (Extended Abstract in Proc. of STACS'97, LNCS 1200, pp.387-398.
4. A. E. Andreev, J. L. Baskakov, A. E. F. Clementi, J. D. P. Rolim (1997), Small Random Sets for Afine Spaces and Better Explicit Lower Bounds for Branching Programs", Electronic Colloquium on Computational Complexity (ECCC), 2nd Re- vision of TR97-053 (http://www.eccc.uni-trier.de/eccc).
5. R. Armoni, M. Saks, A. Wigderson, and S. Zhou (1996), Discrepancy Sets and Pseudorandom Generators for Combinatorial Rectangles", Proc. of IEEE-FOCS, pp. 412-421.
6. Blum M., and Micali S. (1984), How to generate cryptographically strong sequen- ces of pseudorandom bits", SIAM J. of Computing, 13(4), pp. 850-864.
7. A. Borodin (1993), Time-Space Trade-Offs (getting closer to the barrier?)", Proc. of the IV ISAAC, pp. 209-220.
8. A.Borodin, A.Razborov and R.Smolensky (1993), On lower bounds for read-k times branching programs", Computational Complexity, 3, pp. 1-18.
9. L. Fortnow (1997), Nondeterministic polynomial time versus nondeterministic logarithmic space: Time-space tradeofis for satisfiability", Proc. of 12-th IEEE Conference on Computational Complexity, pp. 52-60.
10. R. Impagliazzo, and A. Wigderson (1997), P= BPP if E requires exponential circuits: Derandomizing the XOR lemma" Proc. of ACM STOC, pp. 220-229.
11. S. Jukna (1995), A Note on Read-k-times Branching programs", RAIRO Theoretical Informatics and Applications, 29 (1), pp.75-83. (also in ECCC, TR94-027).
12. Valentine Kabanets (1999), Almost k-Wise Independence and Boolean Functions Hard for Read-Once Branching Programs", ECCC, TR99-004.
13. E. Kushilevitz, and Y. Mansour (1993), Learning Decision Trees Using the Fourier Spectrum", SICOMP 22(6), pp. 1331-1348. Early version: STOC 91.
14. J.Naor, and M.Naor (1990), Small-bias probability spaces: eficient constructions and aplications", Proc. of ACM-STOC, pp. 213-223.
15. E. Neciporuk (1966), On a Boolean Function", Soviet. Math. Doklady, 7, 999-1000.
16. Nisan N., and Wigderson A. (1994), Hardness vs Randomness", J. Comput. System Sci., 49, pp. 149-167.
17. E.A. Okolnishnikova (1993), On lower bounds for branching programs", Siberian Advances in Mathematics, 3(1), pp. 152-166.
18. A.A. Razbarov (1991), Lower Bounds for Deterministic and Nondeterministic Branching Programs", LNCS, 529, pp. 47-61.
19. M. Sauerhoff (1997), A Lower Bound for Randomized Read-k-Times Branching Programs", ECCC, TR97-019.
20. P. Savicky and S. Zak (1996), A large lower bound for 1-branching programs", ECCC, TR96-036 (Revision 01) (to appear in Theoretical Computer Science).
21. P. Savicky and S. Zak (1998), A read-once lower bound and a (1, +k)-hierarchy for branching programs", (to appear in Theoretical Computer Science).
22. J. Simon and M. Szegedy (1993), A new lower bound theorem for read only once branching programs and its applications", Advances in Computational Complexity Theory (J.Cai, editor), AMS-DIMACS Series, 13, pp.183-193.
23. I. Wegener (1987), the Complexity of Boolean Functions, B.G. Teubner, 1 edition.