Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
6874667 | Journal of Computer and System Sciences | 2018 | 13 Pages |
Abstract
Although a simple counting argument shows the existence of Boolean functions of exponential circuit complexity, proving superlinear circuit lower bounds for explicit functions seems to be out of reach of the current techniques. There has been a (very slow) progress in proving linear lower bounds with the latest record of 3186nâo(n). All known lower bounds are based on the so-called gate elimination technique. A typical gate elimination argument shows that it is possible to eliminate several gates from a circuit by making one or several substitutions to the input variables and repeats this inductively. In this paper we prove that this method cannot achieve linear bounds of cn beyond a certain constant c, where c depends only on the number of substitutions made at a single step of the induction.
Keywords
Related Topics
Physical Sciences and Engineering
Computer Science
Computational Theory and Mathematics
Authors
Alexander Golovnev, Edward A. Hirsch, Alexander Knop, Alexander S. Kulikov,