Abstract
We prove an exponential lower bound on the size of static Lovász-Schrijver calculus refutations of Tseitin tautologies. We use several techniques, namely, translating static LS + proof into Positivstellensatz proof of Grigoriev et al., extracting a “good” expander out of a given graph by removing edges and vertices of Alekhnovich et al., and proving linear lower bound on the degree of Positivstellensatz proofs for Tseitin tautologies.
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Kojevnikov, A., Itsykson, D. (2006). Lower Bounds of Static Lovász-Schrijver Calculus Proofs for Tseitin Tautologies. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds) Automata, Languages and Programming. ICALP 2006. Lecture Notes in Computer Science, vol 4051. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11786986_29
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DOI: https://doi.org/10.1007/11786986_29
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