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

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F17%3A00473043" target="_blank" >RIV/67985840:_____/17:00473043 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.1137/15M1018319" target="_blank" >http://dx.doi.org/10.1137/15M1018319</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1137/15M1018319" target="_blank" >10.1137/15M1018319</a>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

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

Projekt

<a href="/cs/project/GBP202%2F12%2FG061" target="_blank" >GBP202/12/G061: Centrum excelence - Institut teoretické informatiky (CE-ITI)</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2017

Kód důvěrnosti údajů

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

Název periodika

Siam Journal on Computing

ISSN

0097-5397

e-ISSN

—

Svazek periodika

46

Číslo periodika v rámci svazku

1

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

18

Strana od-do

114-131

Kód UT WoS článku

000396677400006

EID výsledku v databázi Scopus

2-s2.0-85014494342