In a multi-k-ic depth three circuit every variable appears in at most k of the linear polynomials in every product gate of the circuit. This model is a natural generalization of multilinear depth three circuits that allows the formal degree of the circuit to exceed the number of underlying variables (as the formal degree of a multi-k-ic depth three circuit can be kn where n is the number of variables). The problem of proving lower bounds for depth three circuits with high formal degree has gained in importance following a work by Gupta, Kamath, Kayal and Saptharishi [7] on depth reduction to high formal degree depth three circuits. In this work, we show an exponential lower bound for multi-k-ic depth three circuits for any arbitrary constant k.
@InProceedings{kayal_et_al:LIPIcs.STACS.2015.527, author = {Kayal, Neeraj and Saha, Chandan}, title = {{Multi-k-ic Depth Three Circuit Lower Bound}}, booktitle = {32nd International Symposium on Theoretical Aspects of Computer Science (STACS 2015)}, pages = {527--539}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-939897-78-1}, ISSN = {1868-8969}, year = {2015}, volume = {30}, editor = {Mayr, Ernst W. and Ollinger, Nicolas}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.STACS.2015.527}, URN = {urn:nbn:de:0030-drops-49395}, doi = {10.4230/LIPIcs.STACS.2015.527}, annote = {Keywords: arithmetic circuits, multilinear circuits, depth three circuits, lower bound, individual degree} }
Feedback for Dagstuhl Publishing