A new characterization of ACC(0) and probabilistic CC0

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

A new characterization of ACC(0) and probabilistic CC0

Popis výsledku v původním jazyce

Barrington, Straubing and Therien (1990) conjectured that the Boolean AND function can not be computed by polynomial size constant depth circuits built from modular counting gates, i.e., by CC0 circuits. In this work we show that the AND function can becomputed by uniform probabilistic CC0 circuits that use only O(log n) random bits. This may be viewed as evidence contrary to the conjecture. As a consequence of our construction we get that all of ACC0 can be computed by probabilistic CC0 circuits thatuse only O(log n) random bits. Thus, if one were able to derandomize such circuits, we would obtain a collapse of circuit classes giving ACC0=CC0. We present a derandomization of probabilistic CC0 circuits using AND and OR gates to obtain ACC0 = AND /circ OR /circ CC0 = OR /circ AND /circ CC0. AND and OR gates of sublinear fan-in suffice. Both these results hold for uniform as well as non-uniform circuit classes.

Název v anglickém jazyce

A new characterization of ACC(0) and probabilistic CC0

Popis výsledku anglicky

Barrington, Straubing and Therien (1990) conjectured that the Boolean AND function can not be computed by polynomial size constant depth circuits built from modular counting gates, i.e., by CC0 circuits. In this work we show that the AND function can becomputed by uniform probabilistic CC0 circuits that use only O(log n) random bits. This may be viewed as evidence contrary to the conjecture. As a consequence of our construction we get that all of ACC0 can be computed by probabilistic CC0 circuits thatuse only O(log n) random bits. Thus, if one were able to derandomize such circuits, we would obtain a collapse of circuit classes giving ACC0=CC0. We present a derandomization of probabilistic CC0 circuits using AND and OR gates to obtain ACC0 = AND /circ OR /circ CC0 = OR /circ AND /circ CC0. AND and OR gates of sublinear fan-in suffice. Both these results hold for uniform as well as non-uniform circuit classes.

Druh

D - Stať ve sborníku

CEP obor

BA - Obecná matematika

OECD FORD obor

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Projekt

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

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>Z - Vyzkumny zamer (s odkazem do CEZ)

Rok uplatnění

2009

Kód důvěrnosti údajů

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

Název statě ve sborníku

Proceedings of the 24th Annual IEEE Conference on Computational Complexity

ISBN

978-0-7695-3717-7

ISSN

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e-ISSN

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Počet stran výsledku

8

Strana od-do

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Název nakladatele

IEEE Computer Society

Místo vydání

Los Alamitos

Místo konání akce

Paris

Datum konání akce

15. 7. 2009

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

000273015300004