NDLI: Short Proofs May Be Spacious: An Optimal Separation of Space and Length in Resolution

Content Provider	IEEE Xplore Digital Library
Author	Ben-Sasson, E. Nordstrom, J.
Copyright Year	2008
Description	Author affiliation: Sch. of Comput. Sci. & Commun., R. Inst. of Technol., Stockholm (Nordstrom, J.) \|\| Comput. Sci. Dept. Technion, Technion - Israel Inst. of Technol., Haifa (Ben-Sasson, E.)
Abstract	A number of works have looked at the relationship between length and space of resolution proofs. A notorious question has been whether the existence of a short proof implies the existence of a proof that can be verified using limited space.In this paper we resolve the question by answering it negatively in the strongest possible way. We show that there are families of 6-CNF formulas of size n, for arbitrarily large n, that have resolution proofs of length O(n) but for which any proof requires space Omega(n/log n). This is the strongest asymptotic separation possible since any proof of length O(n) can always be transformed into a proof in space O(n / log n).Our result follows by reducing the space complexity of so called pebbling formulas over a directed acyclic graph to the black-white pebbling price of the graph.The proof is somewhat simpler than previous results (in particular, those reported in [Nordstrom 2006, Nordstrom and Hastad 2008]) as it uses a slightly different flavor of pebbling formulas which allows for a rather straightforward reduction of proof space to standard black-white pebbling price.
Starting Page	709
Ending Page	718
File Size	355293
Page Count	10
File Format	PDF
ISBN	9780769534367
ISSN	02725428
DOI	10.1109/FOCS.2008.42
Language	English
Publisher	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Publisher Date	2008-10-25
Publisher Place	USA
Access Restriction	Subscribed
Rights Holder	Institute of Electrical and Electronics Engineers, Inc. (IEEE)
Subject Keyword	Space technology Computer science Extraterrestrial measurements Length measurement Size measurement Polynomials pebbling games Proof complexity resolution space complexity
Content Type	Text
Resource Type	Article

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