Exponential Lower Bound for Static Semi-algebraic Proofs
نویسندگان
چکیده
Semi-algebraic proof systems were introduced in [1] as extensions of Lovász-Schrijver proof systems [2,3]. These systems are very strong; in particular, they have short proofs of Tseitin’s tautologies, the pigeonhole principle, the symmetric knapsack problem and the cliquecoloring tautologies [1]. In this paper we study static versions of these systems. We prove an exponential lower bound on the length of proofs in one such system. The same bound for two tree-like (dynamic) systems follows. The proof is based on a lower bound on the “Boolean degree” of Positivstellensatz Calculus refutations of the symmetric knapsack problem.
منابع مشابه
Complexity of Semi-algebraic Proofs
It is a known approach to translate propositional formulas into systems of polynomial inequalities and consider proof systems for the latter. The well-studied proof systems of this type are the Cutting Plane proof system (CP) utilizing linear inequalities and the Lovász– Schrijver calculi (LS) utilizing quadratic inequalities. We introduce generalizations LS of LS that operate on polynomial ine...
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