Journal ArticleDOI
The average sensitivity of bounded-depth circuits
Reads0
Chats0
TLDR
It is shown that unbounded-fanin circuits of depth d and size s have average sensitivity O(log s)d−1, and this bound is asymptotically tight.About:
This article is published in Information Processing Letters.The article was published on 1997-09-15. It has received 147 citations till now. The article focuses on the topics: Boolean circuit & Circuit complexity.read more
Citations
More filters
Book
Analysis of Boolean Functions
TL;DR: This text gives a thorough overview of Boolean functions, beginning with the most basic definitions and proceeding to advanced topics such as hypercontractivity and isoperimetry, and includes a "highlight application" such as Arrow's theorem from economics.
Journal ArticleDOI
Complexity measures and decision tree complexity: a survey
Harry Buhrman,Ronald de Wolf +1 more
TL;DR: Several complexity measures for Boolean functions are discussed: certificate complexity, sensitivity, block sensitivity, and the degree of a representing or approximating polynomial, and how they give bounds for the decision tree complexity of Boolean functions on deterministic, randomized, and quantum computers.
Book ChapterDOI
Noise sensitivity of Boolean functions and applications to percolation
TL;DR: In this paper, it was shown that a large class of events in a product probability space are highly sensitive to noise, in the sense that with high probability, the configuration with an arbitrary small percent of random errors gives almost no prediction whether the event occurs.
Proceedings ArticleDOI
Satisfiability Coding Lemma
TL;DR: In this paper, the Satisfiability Coding Lemma is used to encode satisfiable assignments of Boolean formulae in conjunctive normal form with at most /spl kappa/ literals per clause.
References
More filters
Book
Handbook of theoretical computer science
TL;DR: The Handbook of Theoretical Computer Science provides professionals and students with a comprehensive overview of the main results and developments in this rapidly evolving field.
Journal ArticleDOI
Parity, circuits and the polynomial time hierarchy
TL;DR: A super-polynomial lower bound is given for the size of circuits of fixed depth computing the parity function and connections are given to the theory of programmable logic arrays and to the relativization of the polynomial-time hierarchy.
Proceedings ArticleDOI
Parity, circuits, and the polynomial-time hierarchy
TL;DR: A super-polynomial lower bound is given for the size of circuits of fixed depth computing the parity function and connections are given to the theory of programmable logic arrays and to the relativization of the polynomial-time hierarchy.
Journal ArticleDOI
Constant depth circuits, Fourier transform, and learnability
TL;DR: It is shown that an ACO Boolean function has almost all of its "power spectrum" on the low-order coefficients, implying several new properties of functions in -4C(': Functions in AC() have low "average sensitivity;" they may be approximated well by a real polynomial of low degree and they cannot be pseudorandom function generators.