On Derandomizing Tests for Certain Polynomial Identities
نویسنده
چکیده
We extract a paradigm for derandomizing tests for polynomial identities from the recent AKS primality testing algorithm. We then discuss its possible application to other tests.
منابع مشابه
Derandomizing the Isolation Lemma and Lower Bounds for Circuit Size
The isolation lemma of Mulmuley et al [MVV87] is an important tool in the design of randomized algorithms and has played an important role in several nontrivial complexity upper bounds. On the other hand, polynomial identity testing is a well-studied algorithmic problem with efficient randomized algorithms and the problem of obtaining efficient deterministic identity tests has received a lot of...
متن کاملDerandomizing Polynomial Identity over Finite Fields Implies Super-Polynomial Circuit Lower Bounds for NEXP
We show that derandomizing polynomial identity testing over an arbitrary finite field implies that NEXP does not have polynomial size boolean circuits. In other words, for any finite field F (q) of size q, PITq ∈ NSUBEXP ⇒ NEXP ̸⊆ P/poly, where PITq is the polynomial identity testing problem over F (q), and NSUBEXP is the nondeterministic subexpoential time class of languages. Our result is in c...
متن کاملDerandomizing the Isolation Lemma and Lower Bounds for Noncommutative Circuit Size
We give a randomized polynomial-time identity test for noncommutative circuits of polynomial degree based on the isolation lemma. Using this result, we show that derandomizing the isolation lemma implies noncommutative circuit size lower bounds. More precisely, we consider two restricted versions of the isolation lemma and show that derandomizing each of them implies nontrivial circuit size low...
متن کاملOn the Relation between Polynomial Identity Testing and Finding Variable Disjoint Factors
We say that a polynomial f(x1, . . . , xn) is indecomposable if it cannot be written as a product of two polynomials that are defined over disjoint sets of variables. The polynomial decomposition problem is defined to be the task of finding the indecomposable factors of a given polynomial. Note that for multilinear polynomials, factorization is the same as decomposition, as any two different fa...
متن کاملRings with a setwise polynomial-like condition
Let $R$ be an infinite ring. Here we prove that if $0_R$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin X}$ for every infinite subset $X$ of $R$, then $R$ satisfies the polynomial identity $x^n=0$. Also we prove that if $0_R$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in X}$ for every infinite subset $X$ of $R$, then $x^n=x$ for all $xin R$.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2003