Lower bounds on static Lovász-Schrijver calculus proofs for Tseitin tautologies

An exponential lower bound on the size of static Lovász-Schrijver proofs of Tseitin tautologies is established. Several techniques, such as translating a static LS+ proof into a Positivstellensatz proof, extracting a “good” expander out of a given graph by removing edges and vertices, and proving a linear lower bound on the degree of Positivstellensatz proofs for Tseitin tautologies, are used. Bibliography: 22 titles.

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