Lecture 5 : Identity Testing & Isolation Lemma
نویسندگان
چکیده
To use this lemma, we first design a polynomial, p, such that whether p is the 0-polynomial or non-zero is meaningful to us. To differentiate those cases, we choose a set S, set the xi randomly and evaluate p. If p evaluates to something non-zero, then it must be a non-zero polynomial. Conversely if p evaluates to 0, by the lemma, we conclude that it it most likely because p is in fact the 0 polynomial.
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 کاملLecture Notes on Testing Graph Properties in the Dense Graph Model
Organization. The current lecture is the first out of a series of three lectures that cover three models for testing graph properties. In each model, we spell out the definition of property testing (when specialized to that model), present some of the known results, and demonstrate some of the ideas involved (by focusing on testing Bipartiteness, which seems a good benchmark). We start the curr...
متن کاملLecture 01: Randomized Algorithm for Reachability Problem
i.e. with high probability over choices of r, A produces the correct result. It should be noted that the algorithm A itself may not have inherent randomness, rather it might make random calls deterministically. It should also be noted that (1) should hold true for all inputs x, and for most choices of r. Some examples of such algorithms are polynomial identity testing, primality testing (prior ...
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 کاملLecture Notes on Linear Codes Defined over Finite Modules: the Extension Theorem and the Macwilliams Identities — for Use of Cimpa-unesco-tübitak Summer
These lecture notes discuss the extension problem and the MacWilliams identities for linear codes defined over finite modules.
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 2016