A structure theorem for Boolean functions with small total influences
نویسندگان
چکیده
منابع مشابه
A Completeness Theorem for "Total Boolean Functions"
In [3], Christine Tasson introduces an algebraic notion of totality for a denotational model of linear logic. The notion of total boolean function is, in a way, quite intuitive. This note provides a positive answer to the question of completeness of the " boolean centroidal calculus " w.r.t. total boolean functions. 0. Introduction. Even though the question answered in this note has its roots i...
متن کاملA Completeness Theorem for “ Total Boolean Functions ” July 2008
0. Introduction. Even though the question answered in this note has its roots in denotational semantics for the differential λ-calculus ([2] and [1], see also [4]), no background in proof-theory is necessary to understand the problem. In the end, it boils down to a question about a special kind of polynomials in 2n variables over an arbitrary field k. This note is almost “self-contained”, assum...
متن کاملInfluences of monotone Boolean functions
Recently, Keller and Pilpel conjectured that the influence of a monotone Boolean function does not decrease if we apply to it an invertible linear transformation. Our aim in this short note is to prove this conjecture.
متن کاملA quantum algorithm for approximating the influences of Boolean functions
We investigate the influences of variables on a Boolean function f based on the quantum BernsteinVazirani algorithm. A previous paper has proved that if a n-variable Boolean function f(x1, · · · , xn) does not depend on an input variable xi, using the Bernstein-Vazirani circuit to f will always obtain an output y that has a 0 in the ith position. We generalize this result and show that after se...
متن کاملFast Boolean Matching for Small Practical Functions
This paper proposes a fast algorithm for Boolean matching of completely specified Boolean functions. The algorithm can be applied on-the-fly to millions of small practical functions appearing in industrial designs, leading to runtime and memory reduction in logic synthesis and technology mapping. The algorithm is conceptually simpler, faster, and more scalable than previous work.
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: Annals of Mathematics
سال: 2012
ISSN: 0003-486X
DOI: 10.4007/annals.2012.176.1.9