Polynomial size constant depth circuits with a limited number of negations

2005 ◽  
pp. 228-237 ◽  
Author(s):  
Miklos Santha ◽  
Christopher Wilson
Keyword(s):  
Constant Depth ◽  
Polynomial Size ◽  
Constant Depth Circuits

scholarly journals Counting, fanout and the complexity of quantum ACC

2002 ◽  
Vol 2 (1) ◽  
pp. 35-65
Author(s):  
F. Green ◽  
S. Homer ◽  
C. Moore ◽  
C. Pollett
Keyword(s):  
Complexity Classes ◽  
Constant Depth ◽  
Classical Counterpart ◽  
Classical Class ◽  
Polynomial Size ◽  
Constant Depth Circuits ◽  
Language Classes ◽  
Threshold Circuits ◽  
Quantum Analog ◽  
Quantum Complexity

We propose definitions of QAC^0, the quantum analog of the classical class AC^0 of constant-depth circuits with AND and OR gates of arbitrary fan-in, and QACC[q], the analog of the class ACC[q] where Mod_q gates are also allowed. We prove that parity or fanout allows us to construct quantum MOD_q gates in constant depth for any q, so QACC[2] = QACC. More generally, we show that for any q,p > 1, MOD_q is equivalent to MOD_p (up to constant depth and polynomial size). This implies that QAC^0 with unbounded fanout gates, denoted QACwf^0, is the same as QACC[q] and QACC for all q. Since \ACC[p] \ne ACC[q] whenever p and q are distinct primes, QACC[q] is strictly more powerful than its classical counterpart, as is QAC^0 when fanout is allowed. This adds to the growing list of quantum complexity classes which are provably more powerful than their classical counterparts. We also develop techniques for proving upper bounds for QACC in terms of related language classes. We define classes of languages closely related to QACC[2] and show that restricted versions of them can be simulated by polynomial-size circuits. With further restrictions, language classes related to QACC[2] operators can be simulated by classical threshold circuits of polynomial size and constant depth.

Breaking the Minsky--Papert Barrier for Constant-Depth Circuits

2018 ◽  
Vol 47 (5) ◽  
pp. 1809-1857
Author(s):  
Alexander A. Sherstov
Keyword(s):  
Constant Depth ◽  
Constant Depth Circuits

scholarly journals A logic for constant-depth circuits

1984 ◽  
Vol 61 (1) ◽  
pp. 65-74 ◽  
Author(s):  
Yuri Gurevich ◽  
Harry R. Lewis
Keyword(s):  
Constant Depth ◽  
Constant Depth Circuits
Sign in / Sign up

Export Citation Format

Share Document