Some Meet-in-the-Middle Circuit Lower Bounds

We observe that a combination of known top-down and bottom-up lower bound techniques of circuit complexity may yield new circuit lower bounds.

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

[2]  Howard Straubing,et al.  Complex Polynomials and Circuit Lower Bounds for Modular Counting , 1992, LATIN.

[3]  Zhi-Li Zhang,et al.  Computing Symmetric Functions with AND/OR Circuits and a Single MAJORITY Gate , 1993, STACS.

[4]  Frederic Green.  A complex-number Fourier technique for lower bounds on the Mod-m degree , 2000, computational complexity.

[5]  Jacobo Torán,et al.  Complexity classes defined by counting quantifiers , 1991, JACM.

[6]  Jun Tarui.  Degree complexity of Boolean functions and its applications to relativized separations , 1991, [1991] Proceedings of the Sixth Annual Structure in Complexity Theory Conference.

[7]  Avi Wigderson,et al.  Monotone circuits for connectivity require super-logarithmic depth , 1990, STOC '88.

[8]  Shi-Chun Tsai,et al.  Lower Bounds on Representing Boolean Functions as Polynomials in Zm , 1996, SIAM J. Discret. Math..

[9]  Mikael Goldmann,et al.  On the Power of a Threshold Gate at the Top , 1997, Inf. Process. Lett..

[10]  Michael Sipser,et al.  Parity, circuits, and the polynomial-time hierarchy , 1981, 22nd Annual Symposium on Foundations of Computer Science (sfcs 1981).

[11]  Pavel Pudlák,et al.  Computing Boolean functions by polynomials and threshold circuits , 1998, computational complexity.

[12]  P. Beame.  A switching lemma primer , 1994 .

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

[14]  Johan Håstad,et al.  On the power of small-depth threshold circuits , 1991, computational complexity.

[15]  Heribert Vollmer.  Relating Polynomial Time to Constant Depth , 1998, Theor. Comput. Sci..

[16]  Christer Berg,et al.  A Lower Bound for Perceptrons and an Oracle Separation of the PPPH Hierarchy , 1998, J. Comput. Syst. Sci..

[17]  Avi Wigdersony.  N (log N) Lower Bounds on the Size of Depth 3 Threshold Circuits with and Gates at the Bottom , 1993 .

[18]  Alexander A. Razborov,et al.  Natural Proofs , 2007 .

[19]  David A. Mix Barrington,et al.  Representing Boolean functions as polynomials modulo composite numbers , 1992, STOC '92.

[20]  Richard Beigel.  When do extra majority gates help? Polylog (N) majority gates are equivalent to one , 2005, computational complexity.

[21]  J. Håstad.  Computational limitations of small-depth circuits , 1987 .