Pseudorandom bits for constant depth circuits
- Noam Nisan
- … show all 1 hide
Rent the article at a discountRent now
* Final gross prices may vary according to local VAT.Get Access
For every integerd we explicitly construct a family of functions (pseudo-random bit generators) that convert a polylogarithmic number of truly random bits ton bits that appear random to any family of circuits of polynomial size and depthd. The functions we construct are computable by a uniform family of circuits of polynomial size and constant depth. This allows us to simulate randomized constant depth polynomial size circuits inDSPACE(polylog) and inDTIME(2 polylog ). As a corollary we show that the complexity class AM is equal to the class of languages recognizable in NP with a random oracle. Our technique may be applied in order to get pseudo random generators for other complexity classes as well; a further paper  explores these issues.
- L. Adleman: Two theorems on random polynomial time,19th FOCS pp. 75–83, 1978.
- Ajtai, M. (1983) Annals of Pure and Applied Logic 24: pp. 1-48
- M. Ajtai, andM. Ben-Or: A theorem on probabilistic constant depth computations,16th STOC, pp. 571–474, 1984.
- M. Ajtai, andA. Wigderson: Deterministic simulation of probabilistic constant depth circuits26th FOCS, pp. 11–19, 1985.
- L. Babai: Trading group theory for randomness17th STOC, pp. 421–429, 1975.
- C. H. Benett, andJ. Gill: Relative to a random oracleA, P A ≠NP A ≠Co-NP A with probability 1.SIAM J. Comp. 10, 1981.
- Babai, L., Moran, S. (1988) Arthur Merlin games: a randomized proof system, and a hierarchy of complexity classes. J. Computer Sys. Sci. 36: pp. 254-276
- M. Blum, andS. Micali: How to generate cryptographically strong sequences of pseudo random bits.23rd FOCS, pp. 112–117, 1982.
- A. Chandra, D. Kozen, andL. Stockmeyer: Alternation,J. ACM,28, 1981.
- M. Furst, R. J. Lipton, andL. Stoclmeyer: Pseudo random number generation and space complexity,Information and Control,64, 1985.
- M. Furst, J. Saxe, andM. Sipser: Parity, Circuits, and the polynomial time hierarchy,22nd FOCS, pp. 260–270, 1981.
- S. Goldwasser, andS. Micali: Probabilistic Encryption,JCSS,28, No. 2, 1984.
- S. Goldwasser, andM. Sipser: Private coins vs. Public voins in interactive proof systems,18th STOC, pp. 59–68, 1986.
- J. Hastad:Lower Bounds for the Size of Parity Circuits, Ph.D. Thesis, M.I.T., 1987.
- S. A. Kurts: A note on randomized polynomial time,SIAM J. Comp. 16, No. 5, 1987.
- N. Nisan, andA. Wigderson: Hardness vs. Randomness,29th FOCS, 1988.
- J. H. Reif, andJ. D. Tygar: Towards a theory of parallel randomized computation,TR-07-84, Aiken Computation Lab., Harvard University, 1984.
- M. Sipser: A complexity theoretic approach to randomness,15th STOC, 330–335, 1983.
- M. Sipser: Expanders, Randomness, or Time vs. Space, Structure in Complexity Theory, Lecture notes in Computer Science, No. 223, Ed. G. Goos, J. Hartmanis, pp. 325–329.
- L. Stockmeyer: The polynomial time hierarchy,Theory. Comp. Sci. 3, No. 1, 1976.
- A. C. Yao: Theory and applications of trapdoor functions,23rd FOCS, pp. 80–91, 1982.
- A. C. Yao: Separating the polynomial time hierarchy by oracles,26th FOCS, pp. 1–10, 1985.
- Pseudorandom bits for constant depth circuits
Volume 11, Issue 1 , pp 63-70
- Cover Date
- Print ISSN
- Online ISSN
- Additional Links
- 68 C 25
- Industry Sectors
- Noam Nisan (1)
- Author Affiliations
- 1. Department of Computer Science, Hebrew University of Jerusalem, Israel