[Proof Complexity] Preprint
thapen
thapen at math.cas.cz
Wed Apr 10 16:48:38 CEST 2019
Dear colleagues,
Nicola Galesi, Leszek Kolodziejczyk and I have a new preprint,
"Polynomial calculus space and resolution width".
It is on ECCC: https://eccc.weizmann.ac.il/report/2019/052/
The abstract is: We show that if a k-CNF requires width w to refute in
resolution, then it requires space \sqrt{w} to refute in polynomial
calculus, where the space of a polynomial calculus refutation is the
number of monomials that must be kept in memory when working through the
proof. This is the first analogue, in polynomial calculus, of Atserias
and Dalmau's result lower-bounding clause space in resolution by
resolution width.
As a by-product of our new approach to space lower bounds we give a
simple proof of Bonacina's recent result that total space in resolution
(the total number of variable occurrences that must be kept in memory)
is lower-bounded by the width squared. As corollaries of the main result
we obtain some new lower bounds on the PCR space needed to refute
specific formulas, as well as partial answers to some open problems
about relations between space, size, and degree for polynomial calculus.
Comments appreciated,
Best,
Neil
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