Krw composition theorems via lifting

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F20%3A00539556" target="_blank" >RIV/67985840:_____/20:00539556 - isvavai.cz</a>

Result on the web

<a href="http://dx.doi.org/10.1109/FOCS46700.2020.00013" target="_blank" >http://dx.doi.org/10.1109/FOCS46700.2020.00013</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1109/FOCS46700.2020.00013" target="_blank" >10.1109/FOCS46700.2020.00013</a>

Result language

angličtina

Original language name

Krw composition theorems via lifting

Original language description

One of the major open problems in complexity theory is proving super-logarithmic lower bounds on the depth of circuits (i.e., mathrm{P} nsubseteq text{NC}{1}). Karchmer, Raz, and Wigderson [13] suggested to approach this problem by proving that depth complexity behaves'as expected' with respect to the composition of functions f diamond g. They showed that the validity of this conjecture would imply that mathrm{P} nsubseteq text{NC}{1}. Several works have made progress toward resolving this conjecture by proving special cases. In particular, these works proved the KRW conjecture for every outer function, but only for few inner functions. Thus, it is an important challenge to prove the KRW conjecture for a wider range of inner functions. In this work, we extend significantly the range of inner functions that can be handled. First, we consider the monotone version of the KRW conjecture. We prove it for every monotone inner function whose depth complexity can be lower bounded via a query-to-communication lifting theorem. This allows us to handle several new and well-studied functions such as the s-t-connectivity, clique, and generation functions. In order to carry this progress back to the non-monotone setting, we introduce a new notion of semi-monotone composition, which combines the non-monotone complexity of the outer function with the monotone complexity of the inner function. In this setting, we prove the KRW conjecture for a similar selection of inner functions, but only for a specific choice of the outer function f.

Czech name

—

Czech description

—

Type

D - Article in proceedings

CEP classification

—

OECD FORD branch

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Project

—

Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2020

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection

2020 IEEE 61st Annual Symposium on Foundations of Computer Science

ISBN

978-1-7281-9622-0

ISSN

—

e-ISSN

—

Number of pages

7

Pages from-to

43-49

Publisher name

IEEE

Place of publication

Los Alamitos

Event location

Durham

Event date

Nov 16, 2020

Type of event by nationality

WRD - Celosvětová akce

UT code for WoS article

—