Journal of the ACM (JACM)
Linear gaps between degrees for the polynomial calculus modulo distinct primes
Journal of Computer and System Sciences - Special issue on the fourteenth annual IEE conference on computational complexity
Short proofs are narrow—resolution made simple
Journal of the ACM (JACM)
The Cutting Plane Proof System with Bounded Degree of Falsity
CSL '91 Proceedings of the 5th Workshop on Computer Science Logic
Complexity of semialgebraic proofs with restricted degree of falsity
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
A rank lower bound for cutting planes proofs of ramsey's theorem
SAT'13 Proceedings of the 16th international conference on Theory and Applications of Satisfiability Testing
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Goerdt [Goe91] considered a weakened version of the Cutting Plane proof system with a restriction on the degree of falsity of intermediate inequalities. (The degree of falsity of an inequality written in the form ∑aixi + ∑bi(1−xi)≥A, ai,bi≥0 is its constant term A.) He proved a superpolynomial lower bound on the proof length of Tseitin-Urquhart tautologies when the degree of falsity is bounded by $\frac{n}{log^2 n+1}$ (n is the number of variables). In this paper we show that if the degree of falsity of a Cutting Planes proof Π is bounded by d(n) ≤ n/2, this proof can be easily transformed into a resolution proof of length at most |∏| · (d(n)n−1)64d(n). Therefore, an exponential bound on the proof length of Tseitin-Urquhart tautologies in this system for d(n) ≤ cn for an appropriate constant c 0 follows immediately from Urquhart's lower bound for resolution proofs [Urq87].