For every k>1, we give an explicit polynomial that is computable by a linear-sized monotone circuit of width 2k but has no subexponential-sized monotone circuit of width k. As a consequence we show that the constant-width and the constant-depth hierarchies of monotone arithmetic circuits (both commutative and noncommutative) are infinite. We also prove hardness-randomness tradeoffs for identity testing of constant-width circuits analogous to [6,4]. © 2009 Springer-Verlag Berlin Heidelberg.
CITATION STYLE
Arvind, V., Joglekar, P. S., & Srinivasan, S. (2009). On lower bounds for constant width arithmetic circuits. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 5878 LNCS, pp. 637–646). https://doi.org/10.1007/978-3-642-10631-6_65
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