Optimal bounds on the approximation of boolean functions with consequences on the concept of hardness

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

Volumn 1046, Issue , 1996, Pages 319-330

  Andreev, Alexander E ^a   Clementi, Andrea E F ^b   Rolim, José D P ^b  

^a MOSCOW STATE UNIVERSITY   (Russian Federation)

^b UNIVERSITY OF GENEVA   (Switzerland)

Author keywords

[No Author keywords available]

Indexed keywords

HARDNESS; MATHEMATICAL OPERATORS; POLYNOMIAL APPROXIMATION;

APPROXIMATION DEGREES; CIRCUIT SIZE; DOMAIN SIZE; FUNCTION APPROXIMATION; LINEAR OPERATORS; MINIMUM VALUE; OPTIMAL BOUNDS; POLYNOMIAL SIZE;

BOOLEAN FUNCTIONS;

EID: 84947774278     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-60922-9_27     Document Type: Conference Paper

References (19)

1. Allender E. and Strauss M. (1994), "Measure on Small Complexity Classes, with Applications for BPP," Proc. of 35th IEEE FOCS, 819-830.
2. Alon N. and Spencer J.H. (1992), The Probabilistic Method, Wiley-Interscience Publication.
3. Andreev A.E. (1985), "The universal principle of self-correction," Mat. Sbornik 127(169), N 6, 147-172 (in Russian). English transi, in Math. USSR Sbornik, 55 (1), 145-169 (1986).
4. Andreev A.E. (1989), "On the complexity of the realizations of partial boolean functions by circuits of functional elements," J. of Discr. Math, and Appl. 1, 251-262 (1989).
5. Blum M. and Micali S. (1984), "How to generate cryptographically strong sequences of pseudorandom bits," J. SIAM, 13(4), 850-864.
6. Boppana R. and Hirshfield (1989), "Pseudorandom generators and complexity classes," in Randomness and Computation (S. Micali Ed.), 5, 1-26, Adv. in Comput. Res., JAI Press.
7. Chernoff H. (1952), "A measure of asymptotic efficiency for tests of a hypothesis on the sum of observations," Ann. Math. Statistic., 23, 493-507.
8. Feller W. (1970), An Introduction to probability theory and its applications, (Vol. I), III edition, John Wiley and Sons.
9. Hagerup T. and Rub C. (1990), "A guided tour of Chernoff bounds," IPL, 33, 305-308.
10. Kearns M. and Vazirani U. (1994), Topics in Computational Learning Theory, MIT Press.
11. Lupanov O.B. (1965), "About a method circuits design-local coding principle," Problemy Kibernet. 10, 31-110 (in Russian). English Translation in Systems Theory Res., 10, 1963.
12. Nechiporuk E.I. (1965), "About the complexity of gating circuits for the partial boolean matrix," Dokl. Akad. Nauk SSSR, 163, 40-42 (in Russian). English translation in Soviet Math. Docl.
13. Nisan N. (1992), Using Hard Problems to Create Pseudorandom Generators, ACM Distinguished Dissertation, MIT Press.
14. Nisan N. and Wigderson A. (1994), "Hardness vs Randomness," J. Comput. System Sci. 49, 149-167 (presented also at the 29th IEEE FOCS, 1988).
15. Pippenger N. (1977), "Information theory and the complexity of Boolean functions," Math. Systems Theory 10, 129-167.
16. Razborov A. and Rudich S. (1994), "Natural Proofs," Proc. of 26th ACM STOC, 204-213, 1994.
17. Regan K.W., Sivakumar D. and Cai J. (1995), "Pseudorandom Generators, Measure Theory, and Natural Proofs," Proc. of the 36th IEEE FOCS, to appear.
18. Shannon, C.E. (1949), "The synthesis of two-terminal switching circuits," Bell. Syst. Tech. J. 28, 59-98.
19. Yao A.C. (1982), "Theory and applications of trapdoor functions," Proc. Of the 23th IEEE FOCS, 80-91.