AC0 Circuit Complexity

We shall survey several lower bound methods for AC0-circuits including some recent unpublished work. The main methods discussed here include random restrictions, approximations by low degree polynomials, a top-down method based on k-limits and the Fourier transform of boolean functions.

[1]  Johan Håstad,et al.  Almost optimal lower bounds for small depth circuits , 1986, STOC '86.

[2]  Jan van Leeuwen,et al.  Handbook of Theoretical Computer Science, Vol. A: Algorithms and Complexity , 1994 .

[3]  Andrew Chi-Chih Yao,et al.  Separating the Polynomial-Time Hierarchy by Oracles (Preliminary Version) , 1985, FOCS.

[4]  Pavel Pudlák,et al.  Top-down lower bounds for depth 3 circuits , 1993, Proceedings of 1993 IEEE 34th Annual Foundations of Computer Science.

[5]  Leslie G. Valiant,et al.  NP is as easy as detecting unique solutions , 1985, STOC '85.

[6]  Richard Beigel,et al.  The polynomial method in circuit complexity , 1993, [1993] Proceedings of the Eigth Annual Structure in Complexity Theory Conference.

[7]  P. Erdös,et al.  Intersection Theorems for Systems of Sets , 1960 .

[8]  A. Razborov.  Lower bounds on the size of bounded depth circuits over a complete basis with logical addition , 1987 .

[9]  Miklós Ajtai,et al.  ∑11-Formulae on finite structures , 1983, Ann. Pure Appl. Log..

[10]  Ravi B. Boppana,et al.  The Complexity of Finite Functions , 1991, Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity.

[11]  Roman Smolensky,et al.  Algebraic methods in the theory of lower bounds for Boolean circuit complexity , 1987, STOC.

[12]  Mihalis Yannakakis,et al.  On monotone formulae with restricted depth , 1984, STOC '84.

[13]  Peter Frankl,et al.  Complexity classes in communication complexity theory , 1986, 27th Annual Symposium on Foundations of Computer Science (sfcs 1986).

[14]  Avi Wigderson,et al.  Monotone Circuits for Connectivity Require Super-Logarithmic Depth , 1990, SIAM J. Discret. Math..

[15]  Leslie G. Valiant,et al.  Graph-Theoretic Arguments in Low-Level Complexity , 1977, MFCS.

[16]  Michael Sipser,et al.  A Topological View of Some Problems in Complexity Theory , 1984, MFCS.

[17]  Stephan Waack,et al.  Lower bounds for Boolean formulae of depth 3 and the topology of the n-cube (preliminary version) , 1985, FCT.

[18]  James Aspnes,et al.  The expressive power of voting polynomials , 1991, STOC '91.

[19]  Ravi B. Boppana,et al.  Threshold Functions and Bounded Depth Monotone Circuits , 1986, J. Comput. Syst. Sci..

[20]  Noam Nisan,et al.  Constant depth circuits, Fourier transform, and learnability , 1989, 30th Annual Symposium on Foundations of Computer Science.