Monomial size vs. Bit-complexity in Sums-of-Squares and Polynomial Calculus
In this paper we consider the relationship between monomial-size and bit-complexity in Sums-of-Squares (SOS) in Polynomial Calculus Resolution over rationals ({\text{PCR}}/\mathbb{Q}). We show that there is a set of polynomial constraints Q n over Boolean variables that has both SOS and {\text{PCR}}...
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| Published in: | Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science pp. 1 - 7 |
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| Format: | Conference Proceeding |
| Language: | English |
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29.06.2021
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| 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 ({\text{PCR}}/\mathbb{Q}). We show that there is a set of polynomial constraints Q n over Boolean variables that has both SOS and {\text{PCR}}/\mathbb{Q} refutations of degree 2 and thus with only polynomially many monomials, but for which any SOS or {\text{PCR}}/\mathbb{Q} refutation must have exponential bit-complexity, when the rational coefficients are represented with their reduced fractions written in binary. |
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| AbstractList | In this paper we consider the relationship between monomial-size and bit-complexity in Sums-of-Squares (SOS) in Polynomial Calculus Resolution over rationals ({\text{PCR}}/\mathbb{Q}). We show that there is a set of polynomial constraints Q n over Boolean variables that has both SOS and {\text{PCR}}/\mathbb{Q} refutations of degree 2 and thus with only polynomially many monomials, but for which any SOS or {\text{PCR}}/\mathbb{Q} refutation must have exponential bit-complexity, when the rational coefficients are represented with their reduced fractions written in binary. |
| Author | Hakoniemi, Tuomas |
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| Snippet | In this paper we consider the relationship between monomial-size and bit-complexity in Sums-of-Squares (SOS) in Polynomial Calculus Resolution over rationals... |
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| SubjectTerms | Calculus Computer science |
| Title | Monomial size vs. Bit-complexity in Sums-of-Squares and Polynomial Calculus |
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