Short proofs may be spacious: An optimal separation of space and length in resolution
Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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Short proofs may be spacious : An optimal separation of space and length in resolution. / Ben-Sasson, Eli; Nordström, Jakob.
Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008. 2008. s. 709-718 4691003 (Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS).Publikation: Bidrag til bog/antologi/rapport › Konferencebidrag i proceedings › Forskning › fagfællebedømt
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TY - GEN
T1 - Short proofs may be spacious
T2 - 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008
AU - Ben-Sasson, Eli
AU - Nordström, Jakob
PY - 2008
Y1 - 2008
N2 - 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 Ω(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 [Nordström 2006, Nordström and Håstad 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.
AB - 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 Ω(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 [Nordström 2006, Nordström and Håstad 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.
UR - http://www.scopus.com/inward/record.url?scp=57949109817&partnerID=8YFLogxK
U2 - 10.1109/FOCS.2008.42
DO - 10.1109/FOCS.2008.42
M3 - Article in proceedings
AN - SCOPUS:57949109817
SN - 9780769534367
T3 - Proceedings - Annual IEEE Symposium on Foundations of Computer Science, FOCS
SP - 709
EP - 718
BT - Proceedings of the 49th Annual IEEE Symposium on Foundations of Computer Science, FOCS 2008
Y2 - 25 October 2008 through 28 October 2008
ER -
ID: 251871095