Lower bounds for modular counting by circuits with modular gates
We prove that constant depth circuits, with one layer of MOD m gates at the inputs, followed by a fixed number of layers of MOD p gates, where p is prime, require exponential size to compute the MOD q function, if q is a prime that divides neither p nor q.
Unable to display preview. Download preview PDF.
- 5.M. Krause and P. Pudlák, “On the Computational Power of Depth 2 Circuits with Threshold and Modulo Gates”, Proc. 26th ACM STOC (1994) 48–57.Google Scholar
- 6.P. McKenzie, P. Péladeau, and D. Thérien, NC 1: “The Automata-Theoretic Approach”, to appear in Theoretical Computer Science.Google Scholar
- 7.R. Smolensky, “Algebraic Methods in the Theory of Lower Bounds for Boolean Circuit Complexity”, Proc. 19th ACM STOC (1987) 77–82.Google Scholar
- 9.H. Straubing, Finite Automata, Formal Logic and Circuit Complexity, Birkhäuser, Boston, 1994.Google Scholar