Toward better formula lower bounds: The composition of a function and a universal relation

0473043 - MÚ 2018 RIV US eng J - Článek v odborném periodiku
Gavinsky, Dmitry - Meir, O. - Weinstein, O. - Wigderson, A.
Toward better formula lower bounds: The composition of a function and a universal relation.
Siam Journal on Computing. Roč. 46, č. 1 (2017), s. 114-131. ISSN 0097-5397. E-ISSN 1095-7111
Grant CEP: GA ČR GBP202/12/G061
Institucionální podpora: RVO:67985840
Klíčová slova: formula * Karchmer-Wigderson relations * lower bounds
Obor OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Impakt faktor: 0.902, rok: 2017
http://epubs.siam.org/doi/10.1137/15M1018319

One of the major open problems in complexity theory is proving superlogarithmic lower bounds on the depth of circuits (i.e., P ... NC1). This problem is interesting for two reasons: first, it is tightly related to understanding the power of parallel computation and of small-space computation, second, it is one of the first milestones toward proving superpolynomial circuit lower bounds. Karchmer, Raz, and Wigderson [Comput. Complexity, 5 (1995), pp. 191-204] suggested approaching this problem by proving the following conjecture: given two Boolean functions f and g, the depth complexity of the composed function g ... f is roughly the sum of the depth complexities of f and g. They showed that the validity of this conjecture would imply that P ... NC1. As a starting point for studying the composition of functions, they introduced a relation called 'the universal relation' and suggested studying the composition of universal relations.
Trvalý link: http://hdl.handle.net/11104/0270211