On convex complexity measures

0342826 - MÚ 2011 RIV NL eng J - Článek v odborném periodiku
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
Grant CEP: GA AV ČR IAA1019401
Výzkumný záměr: CEZ:AV0Z10190503
Klíčová slova: boolean formula * complexity measure * combinatorial rectangle * convexity
Kód oboru RIV: BA - Obecná matematika
Impakt faktor: 0.838, rok: 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.
Trvalý link: http://hdl.handle.net/11104/0185450