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View all- Göös MHollender AJain SMaystre GPires WRobere RTao R(2024)Separations in Proof Complexity and TFNPJournal of the ACM10.1145/366375871:4(1-45)Online publication date: 9-May-2024
Monomial size vs. bit-complexity in sums-of-squares and polynomial calculus
Article No.: 55, Pages 1 - 7
Abstract
In this paper we consider the relationship between monomial-size and bit-complexity in Sums-of-Squares (SOS) in Polynomial Calculus Resolution over rationals (PCR/Q). We show that there is a set of polynomial constraints Qn over Boolean variables that has both SOS and PCR/Q refutations of degree 2 and thus with only polynomially many monomials, but for which any SOS or PCR/Q refutation must have exponential bit-complexity, when the rational coefficients are represented with their reduced fractions written in binary.
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- Monomial size vs. bit-complexity in sums-of-squares and polynomial calculus
Index terms have been assigned to the content through auto-classification.
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Published: 24 November 2021
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LICS '21: 36th Annual ACM/IEEE Symposium on Logic in Computer Science
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View all- Göös MHollender AJain SMaystre GPires WRobere RTao R(2024)Separations in Proof Complexity and TFNPJournal of the ACM10.1145/366375871:4(1-45)Online publication date: 9-May-2024
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