Definability by constant-depth polynomial-size circuits
نویسندگان
چکیده
منابع مشابه
Definability by Constant-Depth Polynomial-Size Circuits
A function of boolean arguments is symmetric if its value depends solely on the number of l 's among its arguments. In the first part of this paper we partially characterize those symmetric functions that can be computed by constant-depth polynomial-size sequences of boolean circuits, and discuss the complete characterization. (We treat both uniform and non-uniform sequences of circuits.) Our r...
متن کاملLinear-Size Constant-Depth Polylog-Treshold Circuits
We present a simple explicit construction giving unbounded fan-in circuits with $o(n)$ gates and depth $O(r)$ for the threshold function of $n$ variables when the threshold is at most $(log n)^r$, for any integer $r>0$. This improves a result of Atjai and Ben-Or, who showed the existence of circuits of size $n^{O(1)}$. This is the highest threshold for which polynomial-size, constant-depth circ...
متن کاملPermanent Does Not Have Succinct Polynomial Size Arithmetic Circuits of Constant Depth
We show that over fields of characteristic zero there does not exist a polynomial p(n) and a constant-free succinct arithmetic circuit family {Φn}, where Φn has size at most p(n) and depth O(1), such that Φn computes the n × n permanent. A circuit family {Φn} is succinct if there exists a nonuniform Boolean circuit family {Cn} with O(logn) many inputs and size n such that that Cn can correctly ...
متن کاملCounting Hierarchies: Polynomial Time and Constant Depth Circuits
In the spring of 1989, Seinosuke Toda of the University of Electro-Communications in Tokyo, Japan, proved that the polynomial hierarchy is contained in P PP To-89]. In this Structural Complexity Column, we will brieey review Toda's result, and explore how it relates to other topics of interest in computer science. In particular, we will introduce the reader to The Counting Hierarchy: a hierarch...
متن کاملBounded-Depth, Polynomial-Size Circuits for Symmetric Functions
Let ~:= {f~,f2 . . . . } be a family of symmetric Boolean functions, where fn has n Boolean variables, for each n I> 1. L e t / ~ ( n ) be the minimum number of variables offn that each have to be set to constant values so that the resulting function is a constant function. We show that the growth rate o f / ~ ( n ) completely determines whether or not the family ~: is 'good', that is, can be r...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Information and Control
سال: 1986
ISSN: 0019-9958
DOI: 10.1016/s0019-9958(86)80006-7