ECCC-Report TR24-046https://eccc.weizmann.ac.il/report/2024/046Comments and Revisions published for TR24-046en-usThu, 07 Mar 2024 10:54:50 +0200
Paper TR24-046
| Polynomial Calculus sizes over the Boolean and Fourier bases are incomparable |
Sasank Mouli
https://eccc.weizmann.ac.il/report/2024/046For every $n >0$, we show the existence of a CNF tautology over $O(n^2)$ variables of width $O(\log n)$ such that it has a Polynomial Calculus Resolution refutation over $\{0,1\}$ variables of size $O(n^3polylog(n))$ 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 [Sok20] and Razborov.Thu, 07 Mar 2024 10:54:50 +0200https://eccc.weizmann.ac.il/report/2024/046