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Lower bounds for modular counting by circuits with modular gates

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (1995) 911 60-71
DOI: 10.1007/3-540-59175-3_81
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Abstract

We prove that constant depth circuits, with one layer of MOD mgates at the inputs, followed by a fixed number of layers of MOD pgates, where p is prime, require exponential size to compute the MOD qfunction, if q is a prime that divides neither p nor q.

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Barrington, D. M., & Straubing, H. (1995). Lower bounds for modular counting by circuits with modular gates. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 911, pp. 60–71). Springer Verlag. https://doi.org/10.1007/3-540-59175-3_81

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