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Paper:

TR24-046 | 6th March 2024 19:27

Polynomial Calculus sizes over the Boolean and Fourier bases are incomparable

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TR24-046
Authors: Sasank Mouli
Publication: 7th March 2024 10:54
Downloads: 98
Keywords: 


Abstract:

For 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.



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