On convex complexity measures

0342826 - MÚ 2011 RIV NL eng J - Journal Article
Hrubeš, P. - Jukna, S. - Kulikov, A. - Pudlák, Pavel
On convex complexity measures.
Theoretical Computer Science. Roč. 411, 16-18 (2010), s. 1842-1854. ISSN 0304-3975. E-ISSN 1879-2294
R&D Projects: GA AV ČR IAA1019401
Institutional research plan: CEZ:AV0Z10190503
Keywords : boolean formula * complexity measure * combinatorial rectangle * convexity
Subject RIV: BA - General Mathematics
Impact factor: 0.838, year: 2010
http://www.sciencedirect.com/science/article/pii/S0304397510000885

Khrapchenko's classical lower bound n(2) on the formula size of the parity function f can be interpreted as designing a suitable measure of sub-rectangles of the combinatorial rectangle f(-1)(0) x f(-1)(1). Trying to generalize this approach we arrived at the concept of convex measures. We prove the negative result that convex measures are bounded by O(n(2)) and show that several measures considered for proving lower bounds on the formula size are convex. We also prove quadratic upper bounds on a class of measures that are not necessarily convex.
Permanent Link: http://hdl.handle.net/11104/0185450