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# Proof complexity in algebraic systems and bounded depth Frege systems with modular counting

@article{Buss1997ProofCI, title={Proof complexity in algebraic systems and bounded depth Frege systems with modular counting}, author={Samuel R. Buss and Russell Impagliazzo and Jan Kraj{\'i}cek and Pavel Pudl{\'a}k and Alexander A. Razborov and Jir{\'i} Sgall}, journal={computational complexity}, year={1997}, volume={6}, pages={256-298} }

- Published 1997 in computational complexity
DOI:10.1007/BF01294258

We prove a lower bound of the formN Ω(1) on the degree of polynomials in a Nullstellensatz refutation of theCount q polynomials over ℤ m , whereq is a prime not dividingm. In addition, we give an explicit construction of a degreeN Ω(1) design for theCount q principle over ℤ m . As a corollary, using Beameet al. (1994) we obtain a lower bound of the form 2 NΩ(1) for the number of formulas in a constant-depth Frege proof of the modular counting principleCount q N from instances of the counting… CONTINUE READING

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