refs.bib

@article{raz,
  title = {Lower Bounds for the Polynomial Calculus},
  author = {Razborov, A.A.},
  date = {1998-12-02},
  journaltitle = {Computational Complexity},
  shortjournal = {Computational Complexity},
  volume = {7},
  number = {4},
  pages = {291--324},
  issn = {1016-3328, 1420-8954},
  doi = {10.1007/s000370050013},
  url = {http://link.springer.com/10.1007/s000370050013},
  urldate = {2022-10-18},
  langid = {english},
  file = {D\:\\Zotero\\storage\\BIQDT3PU\\Razborov - 1998 - Lower bounds for the polynomial calculus.pdf}
}

@article{buss,
  title = {Proof Complexity in Algebraic Systems and Bounded Depth {{Frege}} Systems with Modular Counting},
  author = {Buss, S. and Impagliazzo, R. and Krajíček, J. and Pudlák, P. and Razborov, A. A. and Sgall, J.},
  date = {1996-09-01},
  journaltitle = {Computational Complexity},
  shortjournal = {Comput Complexity},
  volume = {6},
  number = {3},
  pages = {256--298},
  issn = {1420-8954},
  doi = {10.1007/BF01294258},
  url = {https://doi.org/10.1007/BF01294258},
  urldate = {2023-01-18},
  abstract = {We prove a lower bound of the formNΩ(1) on the degree of polynomials in a Nullstellensatz refutation of theCountqpolynomials over ℤm, whereq is a prime not dividingm. In addition, we give an explicit construction of a degreeNΩ(1)design for theCountqprinciple over ℤm. As a corollary, using Beameet al. (1994) we obtain a lower bound of the form 2NΩ(1) for the number of formulas in a constant-depth Frege proof of the modular counting principleCountqNfrom instances of the counting principleCountmM.},
  langid = {english},
  file = {D\:\\Zotero\\storage\\UGXNPM76\\Buss et al. - 1996 - Proof complexity in algebraic systems and bounded .pdf}
}