Pseudo-solutions of polynomial systems and the lower bound problem for $\mbox{AC}^0[p]$-Frege systems
Year: 2026
Type: preprint
Abstract: The problem to establish a lower bound for $\mbox{AC}^0[p]$-Frege refutations of a system of polynomial equations over ${\bf F}_p$ was in K. (2024) reduced to the existence of a pseudo-solution (a notion defined there) for the system. Here we reduce this further, for the system expressing the negation of the PHP, to a property of search trees querying values of linear maps on the vector space of low degree polynomials over ${\bf F}_p$.
Source: arXiv (Cornell University)
Author: Krajicek, Jan
Institution: Charles University
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214996366