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

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    0473043 - MÚ 2018 RIV US eng J - Journal Article
    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
    R&D Projects: GA ČR GBP202/12/G061
    Institutional support: RVO:67985840
    Keywords : formula * Karchmer-Wigderson relations * lower bounds
    OECD category: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
    Impact factor: 0.902, year: 2017

    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.
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