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Author Bonacina, Ilario ♦ Galesi, Nicola
Source ACM Digital Library
Content type Text
Publisher Association for Computing Machinery (ACM)
File Format PDF
Copyright Year ©2015
Language English
Subject Domain (in DDC) Computer science, information & general works ♦ Data processing & computer science
Subject Keyword Proof complexity ♦ Algebraic proof systems ♦ Polynomial calculus ♦ Random formulae ♦ Resolution ♦ Space complexity
Abstract Algebraic proof systems, such as Polynomial Calculus (PC) and Polynomial Calculus with Resolution (PCR), refute contradictions using polynomials. Space complexity for such systems measures the number of distinct monomials to be kept in memory while verifying a proof. We introduce a new combinatorial framework for proving space lower bounds in algebraic proof systems. As an immediate application, we obtain the space lower bounds previously provided for PC/PCR [Alekhnovich et al. 2002; Filmus et al. 2012]. More importantly, using our approach in its full potential, we prove $Ω(\textit{n})$ space lower bounds in PC/PCR for random $\textit{k}-CNFs$ $(\textit{k}≥$ 4) in $\textit{n}$ variables, thus solving an open problem posed in Alekhnovich et al. [2002] and Filmus et al. [2012]. Our method also applies to the Graph Pigeonhole Principle, which is a variant of the Pigeonhole Principle defined over a constant (left) degree expander graph.
ISSN 00045411
Age Range 18 to 22 years ♦ above 22 year
Educational Use Research
Education Level UG and PG
Learning Resource Type Article
Publisher Date 2015-06-01
Publisher Place New York
e-ISSN 1557735X
Journal Journal of the ACM (JACM)
Volume Number 62
Issue Number 3
Page Count 20
Starting Page 1
Ending Page 20


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Source: ACM Digital Library