[Proof Complexity] New preprint
Iddo Tzameret
iddo.tzameret at gmail.com
Sat May 4 13:10:30 CEST 2013
Dear colleagues,
A new preprint of mine, titled
"On Sparser Random 3SAT Refutation Algorithms and Feasible Interpolation"
is available at: http://iiis.tsinghua.edu.cn/~tzameret/AutFKO.pdf
Comments, corrections, and suggestions are appreciated.
Best wishes,
Iddo Tzameret
--------------------------------------
Abstract: We formalize a combinatorial principle, called the 3XOR
principle, due to Feige, Kim
and Ofek [FKO06], as a family of unsatisfiable propositional formulas
for which refutations
of small size in any propositional proof system that possesses the
feasible interpolation
property imply an efficient deterministic refutation algorithm for
random 3SAT with n
variables and Ω(n^{1.4}) clauses. Such small size refutations would
improve the current best
(with respect to the clause density) efficient refutation algorithm,
which works only for
Ω(n^{1.5}) many clauses [FO07].
We then study the proof complexity of the above formulas in weak
extensions of cutting
planes and resolution. Specifically, we show that there are
polynomial-size refutations
of the 3XOR principle in resolution operating with disjunctions of
quadratic equations
(with small integer coefficients), denoted R(quad). We show that R(quad)
is weakly
automatizable iff R(lin) is weakly automatizable, where R(lin) is
similar to R(quad) but with
linear instead of quadratic equations (introduced in [RT08]). This
reduces the question of the
existence of efficient deterministic refutation algorithms for random
3SAT with n variables
and Ω(n^{1.4}) clauses to the question of feasible interpolation of
R(quad) and to the weak
automatizability of R(lin).
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