TY - GEN

T1 - Exponential lower bound for static semi-algebraic proofs

AU - Grigoriev, Dima

AU - Hirsch, Edward A.

AU - Pasechnik, Dmitrii V.

PY - 2002

Y1 - 2002

N2 - 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.W e 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.

AB - 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.W e 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.

UR - http://www.scopus.com/inward/record.url?scp=72949098117&partnerID=8YFLogxK

U2 - 10.1007/3-540-45465-9_23

DO - 10.1007/3-540-45465-9_23

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AN - SCOPUS:72949098117

SN - 3540438645

SN - 9783540438649

T3 - Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

SP - 257

EP - 268

BT - Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings

A2 - Widmayer, Peter

A2 - Eidenbenz, Stephan

A2 - Triguero, Francisco

A2 - Morales, Rafael

A2 - Conejo, Ricardo

A2 - Hennessy, Matthew

T2 - 29th International Colloquium on Automata, Languages, and Programming, ICALP 2002

Y2 - 8 July 2002 through 13 July 2002

ER -