Abstract
The degree of falsity of an inequality in Boolean variables shows how many variables are enough to substitute in order to satisfy the inequality. Goerdt introduced a weakened version of the Cutting Plane (CP) proof system with a restriction on the degree of falsity of intermediate inequalities [6]. He proved an exponential lower bound for CP proofs with degree of falsity bounded by n/(log^2n+1) , where n is the number of variables In this paper we strengthen this result by establishing a direct connection between CP and Resolution proofs. This result implies an exponential lower bound on the proof length of Tseitin-Urquhart tautologies when the degree of falsity is bounded by cn for some constant c. We also generalize the notion of degree of falsity for extensions of Lov sz-Schrijver calculi a (LS), namely for LSk +CPk proof systems introduced by Grigoriev et al. [8]. We show that any LSk +CPk proof with bounded degree of falsity can be transformed into a Res(k) proof. We also prove lower and upper bounds on the proof length of tautologies in LSk +CPk with bounded degree of falsity.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal on Satisfiability, Boolean Modeling and Computation
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
