Year: 2024
Type: conference-paper
Abstract: For every$n > 0$, we show the existence of a CNF tautology over$O(n^{2})$variables of width$O(\log {\it n})$such that it has a Polynomial Calculus Resolution refutation over$\{0,1\}$variables of size$O(n^{3} \text{polylog} (n))$but any Polynomial Calculus refutation over$\{+1, -1\}$variables requires size$2^{\Omega(n)}$. This shows that Polynomial Calculus sizes over the {0, 1} and$\{+1,\ -1\}$bases are incomparable (since Tseitin tautologies show a separation in the other direction) and answers an open problem posed by Sokolov [1] and Razborov [2].
Author: Sasank Mouli
Institution: Indian Institute of Technology Indore
Language: English
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W4404849204