A new characterization of ACC(0) and probabilistic CC0

0336102 - MÚ 2010 RIV US eng C - Conference Paper (international conference)
Hansen, K.A. - Koucký, Michal
A new characterization of ACC(0) and probabilistic CC0.
Proceedings of the 24th Annual IEEE Conference on Computational Complexity. Los Alamitos: IEEE Computer Society, 2009, s. 27-34. ISBN 978-0-7695-3717-7. ISSN 1093-0159.
[24th Annual IEEE Conference on Computational Complexity. Paris (FR), 15.07.2009-18.07.2009]
R&D Projects: GA ČR GP201/07/P276; GA AV ČR IAA100190902; GA MŠMT(CZ) 1M0545
Institutional research plan: CEZ:AV0Z10190503
Keywords : bounded depth circuits * counting circuits
Subject RIV: BA - General Mathematics

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 be computed 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 that use 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.
Permanent Link: http://hdl.handle.net/11104/0180415