Counting Axioms Do Not Polynomially Simulate Counting Gates
نویسندگان
چکیده
For every prime m ≥ 2, we give a family of tautologies that require super-polynomial size constant-depth Frege proofs from Countm axioms, and whose algebraic translations have constant-degree, polynomial size polynomial calculus refutations over Zm. This shows that constant-depth Frege systems with counting axioms modulo m do not polynomially simulate constant-depth Frege systems with counting gates modulo m. Our primary technical tool is a switching lemma that uses random substitutions of one variable for another in addition to random 0/1 restrictions.
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