Abstract
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 clique-coloring 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.
Partially supported by grant of RAS contest-expertise of young scientists projects and grants from CRDF (RM1-2409-ST-02), RFBR (02-01-00089), and NATO.
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Grigoriev, D., Hirsch, E.A., Pasechnik, D.V.: Complexity of semi-algebraic proofs. Technical Report 01-103, Revision 01, Electronic Colloquim on Computational Complexity (2002) ftp://ftp.eccc.uni-trier.de/pub/eccc/reports/2001/TR01-103/index. html#R01
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Grigoriev, D., Hirsch, E.A., Pasechnik, D.V. (2002). Exponential Lower Bound for Static Semi-algebraic Proofs. In: Widmayer, P., Eidenbenz, S., Triguero, F., Morales, R., Conejo, R., Hennessy, M. (eds) Automata, Languages and Programming. ICALP 2002. Lecture Notes in Computer Science, vol 2380. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45465-9_23
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DOI: https://doi.org/10.1007/3-540-45465-9_23
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