Understanding space in resolution: Optimal lower bounds and exponential trade-offs
E Ben-Sasson, J Nordström - 2008 - drops.dagstuhl.de
We continue the study of tradeoffs between space and length of resolution proofs and focus
on two new results: begin {enumerate} item We show that length and space in resolution are
uncorrelated. This is proved by exhibiting families of CNF formulas of size $ O (n) $ that have
proofs of length $ O (n) $ but require space $ Omega (n/log n) $. Our separation is the
strongest possible since any proof of length $ O (n) $ can always be transformed into a proof
in space $ O (n/log n) $, and improves previous work reported in [Nordstr"{o} m 2006 …
on two new results: begin {enumerate} item We show that length and space in resolution are
uncorrelated. This is proved by exhibiting families of CNF formulas of size $ O (n) $ that have
proofs of length $ O (n) $ but require space $ Omega (n/log n) $. Our separation is the
strongest possible since any proof of length $ O (n) $ can always be transformed into a proof
in space $ O (n/log n) $, and improves previous work reported in [Nordstr"{o} m 2006 …
[PDF][PDF] Understanding Space in Resolution: Optimal Lower Bounds and Exponential Trade-offs
J Nordström - 2008 - people.csail.mit.edu
… Lower bounds: no algorithm can do better (even optimal one always guessing the right
move) Upper bounds: gives hope for good algorithms if we can search for proofs in system
efficiently … Polynomial-size CNF formula family with (weakly) exponential lower bound on
refutation length (pigeonhole principle) …
move) Upper bounds: gives hope for good algorithms if we can search for proofs in system
efficiently … Polynomial-size CNF formula family with (weakly) exponential lower bound on
refutation length (pigeonhole principle) …
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