A Polynomial-time Construction of a Hitting Set for Read-once Branching Programs of Width 3

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F21%3A00367350" target="_blank" >RIV/67985807:_____/21:00367350 - isvavai.cz</a>

Výsledek na webu

<a href="http://dx.doi.org/10.3233/FI-2021-2101" target="_blank" >http://dx.doi.org/10.3233/FI-2021-2101</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.3233/FI-2021-2101" target="_blank" >10.3233/FI-2021-2101</a>

Jazyk výsledku

angličtina

Název v původním jazyce

A Polynomial-time Construction of a Hitting Set for Read-once Branching Programs of Width 3

Popis výsledku v původním jazyce

Recently, an interest in constructing pseudorandom or hitting set generators for restricted branching programs has increased, which is motivated by the fundamental issue of derandomizing space-bounded computations. Such constructions have been known only in the case of width 2 and in very restricted cases of bounded width. In this paper, we characterize the hitting sets for read-once branching programs of width 3 by a so-called richness condition. Namely, we show that such sets hit the class of read-once conjunctions of DNF and CNF (i.e. the weak richness). Moreover, we prove that any rich set extended with all strings within Hamming distance of 3 is a hitting set for read-once branching programs of width 3. Then, we show that any almost O(log n)-wise independent set satisfies the richness condition. By using such a set due to Alon et al. (1992) our result provides an explicit polynomial-time construction of a hitting set for read-once branching programs of width 3 with acceptance probability epsilon>5/6. We announced this result at conferences more than ten years ago, including only proof sketches, which motivated a number of subsequent results on pseudorandom generators for restricted read-once branching programs. This paper contains our original detailed proof that has not been published yet.

Název v anglickém jazyce

A Polynomial-time Construction of a Hitting Set for Read-once Branching Programs of Width 3

Popis výsledku anglicky

Recently, an interest in constructing pseudorandom or hitting set generators for restricted branching programs has increased, which is motivated by the fundamental issue of derandomizing space-bounded computations. Such constructions have been known only in the case of width 2 and in very restricted cases of bounded width. In this paper, we characterize the hitting sets for read-once branching programs of width 3 by a so-called richness condition. Namely, we show that such sets hit the class of read-once conjunctions of DNF and CNF (i.e. the weak richness). Moreover, we prove that any rich set extended with all strings within Hamming distance of 3 is a hitting set for read-once branching programs of width 3. Then, we show that any almost O(log n)-wise independent set satisfies the richness condition. By using such a set due to Alon et al. (1992) our result provides an explicit polynomial-time construction of a hitting set for read-once branching programs of width 3 with acceptance probability epsilon>5/6. We announced this result at conferences more than ten years ago, including only proof sketches, which motivated a number of subsequent results on pseudorandom generators for restricted read-once branching programs. This paper contains our original detailed proof that has not been published yet.

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

Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2021

Kód důvěrnosti údajů

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

Název periodika

Fundamenta Informaticae

ISSN

0169-2968

e-ISSN

1875-8681

Svazek periodika

184

Číslo periodika v rámci svazku

4

Stát vydavatele periodika

NL - Nizozemsko

Počet stran výsledku

48

Strana od-do

307-354

Kód UT WoS článku

000768542000003

EID výsledku v databázi Scopus

2-s2.0-85127188809