Ch. Papadimitriou et M. Yannakakis, ON LIMITED NONDETERMINISM AND THE COMPLEXITY OF THE V-C DIMENSION, Journal of computer and system sciences, 53(2), 1996, pp. 161-170
Citations number
23
Categorie Soggetti
System Science","Computer Science Hardware & Architecture","Computer Science Theory & Methods
We characterize precisely the complexity of several natural computatio
nal problems in NP, which have been proposed but not categorized satis
factorily in the literature: Computing the Vapnik-Chervonenkis dimensi
on of a 0-1 matrix; finding the minimum dominating set of a tournament
; satisfying a Boolean expression by perturbing the default truth assi
gnment; and several others. These problems can be solved in n(O(log n)
) time, and thus, they are probably not NP-complete. We define two new
complexity classes between P and NP, very much in the spirit of MAXNP
and MAXSNP. We show that computing the V-C dimension is complete for
the more general class, while the other two problems are complete for
the weaker class. (C) 1996 Academic Press. Inc.