A Note on MODp - MODm Circuits

We give a new proof of recent results of Grolmusz and Tardos on the computing power of constant-depth circuits consisting of a single layer of $MOD_m$ gates followed by a fixed number of layers of $MOD_{p^k}$-gates, where p is prime.

[1]  Howard Straubing,et al.  Lower bounds for modular counting by circuits with modular gates , 1995, computational complexity.

[2]  Gábor Tardos,et al.  Lower Bounds for (MODp-MODm) Circuits , 2000, SIAM J. Comput..

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

[4]  Pavel Pudlák,et al.  On the Computational Power of Depth-2 Circuits with Threshold and Modulo Gates , 1997, Theor. Comput. Sci..

[5]  Gábor Tardos,et al.  Lower bounds for (MOD p-MOD m) circuits , 1998, Proceedings 39th Annual Symposium on Foundations of Computer Science (Cat. No.98CB36280).

[6]  Denis Thérien,et al.  Non-Uniform Automata Over Groups , 1987, Inf. Comput..

[7]  Howard Straubing,et al.  Non-Uniform Automata Over Groups , 1990, Inf. Comput..

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

[9]  Ronald Fagin,et al.  Bounded-Depth, Polynomial-Size Circuits for Symmetric Functions , 1985, Theoretical Computer Science.