Exponential lower bound for static semi-algebraic proofs

Dima Grigoriev; Edward A. Hirsch; Dmitrii V. Pasechnik

doi:10.1007/3-540-45465-9_23

Exponential lower bound for static semi-algebraic proofs

Dima Grigoriev
, Edward A. Hirsch
, Dmitrii V. Pasechnik

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

11 Scopus citations

Abstract

Semi-algebraic proof systems were introduced in as extensions of Lovász-Schrijver proof systems. 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. 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.

Original language	English
Title of host publication	Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings
Editors	Peter Widmayer, Stephan Eidenbenz, Francisco Triguero, Rafael Morales, Ricardo Conejo, Matthew Hennessy
Pages	257-268
Number of pages	12
DOIs	https://doi.org/10.1007/3-540-45465-9_23
State	Published - 2002
Externally published	Yes
Event	29th International Colloquium on Automata, Languages and Programming, ICALP 2002 - Malaga, Spain Duration: 8 Jul 2002 → 13 Jul 2002

Publication series

Name	Lecture Notes in Computer Science
Volume	2380
ISSN (Print)	0302-9743
ISSN (Electronic)	1611-3349

Conference

Conference	29th International Colloquium on Automata, Languages and Programming, ICALP 2002
Country/Territory	Spain
City	Malaga
Period	8/07/02 → 13/07/02

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10.1007/3-540-45465-9_23

Cite this

Grigoriev, D., Hirsch, E. A., & Pasechnik, D. V. (2002). Exponential lower bound for static semi-algebraic proofs. In P. Widmayer, S. Eidenbenz, F. Triguero, R. Morales, R. Conejo, & M. Hennessy (Eds.), Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings (pp. 257-268). (Lecture Notes in Computer Science; Vol. 2380). https://doi.org/10.1007/3-540-45465-9_23

Grigoriev, Dima ; Hirsch, Edward A. ; Pasechnik, Dmitrii V. / Exponential lower bound for static semi-algebraic proofs. Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings. editor / Peter Widmayer ; Stephan Eidenbenz ; Francisco Triguero ; Rafael Morales ; Ricardo Conejo ; Matthew Hennessy. 2002. pp. 257-268 (Lecture Notes in Computer Science).

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title = "Exponential lower bound for static semi-algebraic proofs",

abstract = "Semi-algebraic proof systems were introduced in as extensions of Lov{\'a}sz-Schrijver proof systems. These systems are very strong; in particular, they have short proofs of Tseitin{\textquoteright}s tautologies, the pigeonhole principle, the symmetric knapsack problem and the cliquecoloring tautologies. 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.",

author = "Dima Grigoriev and Hirsch, \{Edward A.\} and Pasechnik, \{Dmitrii V.\}",

note = "Publisher Copyright: {\textcopyright} Springer-Verlag Berlin Heidelberg 2002.; 29th International Colloquium on Automata, Languages and Programming, ICALP 2002 ; Conference date: 08-07-2002 Through 13-07-2002",

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isbn = "3540438645",

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}

Grigoriev, D, Hirsch, EA & Pasechnik, DV 2002, Exponential lower bound for static semi-algebraic proofs. in P Widmayer, S Eidenbenz, F Triguero, R Morales, R Conejo & M Hennessy (eds), Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings. Lecture Notes in Computer Science, vol. 2380, pp. 257-268, 29th International Colloquium on Automata, Languages and Programming, ICALP 2002, Malaga, Spain, 8/07/02. https://doi.org/10.1007/3-540-45465-9_23

Exponential lower bound for static semi-algebraic proofs. / Grigoriev, Dima; Hirsch, Edward A.; Pasechnik, Dmitrii V.
Automata, Languages and Programming - 29th International Colloquium, ICALP 2002, Proceedings. ed. / Peter Widmayer; Stephan Eidenbenz; Francisco Triguero; Rafael Morales; Ricardo Conejo; Matthew Hennessy. 2002. p. 257-268 (Lecture Notes in Computer Science; Vol. 2380).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › peer-review

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AB - Semi-algebraic proof systems were introduced in as extensions of Lovász-Schrijver proof systems. 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. 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.

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Exponential lower bound for static semi-algebraic proofs

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