ECCC-Report TR09-122https://eccc.weizmann.ac.il/report/2009/122Comments and Revisions published for TR09-122en-usMon, 23 Nov 2009 13:28:35 +0200
Paper TR09-122
| Circuit Lower Bounds, Help Functions, and the Remote Point Problem |
Vikraman Arvind,
Srikanth Srinivasan
https://eccc.weizmann.ac.il/report/2009/122We investigate the power of Algebraic Branching Programs (ABPs) augmented with help polynomials, and constant-depth Boolean circuits augmented with help functions. We relate the problem of proving explicit lower bounds in both these models to the Remote Point Problem (introduced by Alon, Panigrahy, and Yekhanin (RANDOM '09)). More precisely, proving lower bounds for ABPs with help polynomials is related to the Remote Point Problem w.r.t. the rank metric, and for constant-depth circuits with help functions it is related to the Remote Point Problem w.r.t. the Hamming metric. For algebraic branching programs with help polynomials with some degree restrictions we show exponential size lower bounds for explicit polynomials.Mon, 23 Nov 2009 13:28:35 +0200https://eccc.weizmann.ac.il/report/2009/122