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 -