Sums of Read-Once Formulas: How Many Summands Suffice?
نویسندگان
چکیده
An arithmetic read-once formula (ROF) is a formula (circuit of fan-out 1) over +,× where each variable labels at most one leaf. Every multilinear polynomial can be expressed as the sum of ROFs. In this work, we prove, for certain multilinear polynomials, a tight lower bound on the number of summands in such an expression.
منابع مشابه
Read-once polynomials: How many summands suffice?
An arithmetic read-once formula (ROF) is a formula (circuit of fan-out 1) over +,× where each variable labels at most one leaf. Every multilinear polynomial can be expressed as the sum of ROFs. In this work, we prove, for certain multilinear polynomials, a tight lower bound on the number of summands in such an expression.
متن کاملSmall space analogues of Valiant's classes and the limitations of skew formula
In the uniform circuit model of computation, the width of a boolean circuit exactly characterises the “space” complexity of the computed function. Looking for a similar relationship in Valiant’s algebraic model of computation, we propose width of an arithmetic circuit as a possible measure of space. We introduce the class VL as an algebraic variant of deterministic log-space L. In the uniform s...
متن کاملInterpolating Arithmetic Read-Once Formulas in Parallel
A formula is read-once if each variable appears at most once in it. An arithmetic read-once formula is one in which the operations are addition, subtraction, multiplication, and division (and constants are allowed). We present a randomized (Las Vegas) parallel algorithm for the exact interpolation of arithmetic read-once formulas over suuciently large elds. More speciically, for n-variable read...
متن کاملDistorted Sums of Models
Distorted sums of models were introduced and discussed in [Sh2]. This notion generalizes the notion of disjoint (or direct) sums of models by letting the summands overlap. In the first section we investigate types in distorted sums and show that the type of a sequence of elements ¯ a is determined by the 'local' type of ¯ a (i.e. the type restricted to a neighborhood of ¯ a). We simplify the pr...
متن کاملDirect-sum Decompositions over Local Rings
Let (R,m) be a local ring (commutative and Noetherian). If R is complete (or, more generally, Henselian), one has the Krull-Schmidt uniqueness theorem for direct sums of indecomposable finitely generated R-modules. By passing to the m-adic completion b R, we can get a measure of how badly the Krull-Schmidt theorem can fail for a more general local ring. We assign to each finitely generated R-mo...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2015