Homogenization and the polynomial calculus

  title={Homogenization and the polynomial calculus},
  author={Joshua Buresh-Oppenheim and Matthew Clegg and Russell Impagliazzo and Toniann Pitassi},
  journal={computational complexity},
In standard implementations of the Gröbner basis algorithm, the original polynomials are homogenized so that each term in a given polynomial has the same degree. In this paper, we study the effect of homogenization on the proof complexity of refutations of polynomials derived from Boolean formulas in both the Polynomial Calculus (PC) and Nullstellensatz systems. We show that the PC refutations of homogenized formulas give crucial information about the complexity of the original formulas. The… CONTINUE READING
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