Lower Bounds on Testing Functions of Low Fourier Degree

نویسنده

  • Pooya Hatami
چکیده

We consider the problem of testing whether a Boolean function has Fourier degree ≤ k or it is ǫ-far from any Boolean function with Fourier degree ≤ k, we improve the known lower bound of Ω(k) [4, 6], to Ω(k/ √ ǫ). The lower bound uses the recently discovered connections between property testing and communication complexity by Blais et. al. [4]

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Testing Properties of Boolean Functions: Lower Bounds on Testing Fourier Degree

We consider the problem of deciding whether a given object has a given property or it is far from any object with the property, referred to as property testing. We focus on the case where the objects are Boolean functions, and we survey some of the previously known results about testing for properties such as the number of relevant variables and Fourier degree of a Boolean function. We present ...

متن کامل

Testing Properties of Linear Functions

The function f : F2 → F2 is k-linear if it returns the sum (over F2) of exactly k coordinates of its input. We introduce strong lower bounds on the query complexity for testing whether a function is k-linear. We show that for any k ≤ n 2 , at least k−o(k) queries are required to test k-linearity, and we show that when k ≈ n 2 , this lower bound is nearly tight since 4 3 k+o(k) queries are suffi...

متن کامل

Nonclassical Polynomials as a Barrier to Polynomial Lower Bounds

The problem of constructing explicit functions which cannot be approximated by low degree polynomials has been extensively studied in computational complexity, motivated by applications in circuit lower bounds, pseudo-randomness, constructions of Ramsey graphs and locally decodable codes. Still, most of the known lower bounds become trivial for polynomials of superlogarithmic degree. Here, we s...

متن کامل

Distance-Sensitive Property Testing Lower Bounds

In this paper, we consider several property testing problems and ask how the query complexity depends on the distance parameter ǫ. We achieve new lower bounds in this setting for the problems of testing whether a function is monotone and testing whether the function has low Fourier degree. For monotonicity testing, our lower bound matches the recent upper bound of Chakrabarty and Seshadhri [12].

متن کامل

Upper and lower bounds of symmetric division deg index

Symmetric Division Deg index is one of the 148 discrete Adriatic indices that showed good predictive properties on the testing sets provided by International Academy of Mathematical Chemistry. Symmetric Division Deg index is defined by $$ SDD(G) = sumE left( frac{min{d_u,d_v}}{max{d_u,d_v}} + frac{max{d_u,d_v}}{min{d_u,d_v}} right), $$ where $d_i$ is the degree of vertex $i$ in graph $G$. In th...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

عنوان ژورنال:
  • CoRR

دوره abs/1202.3479  شماره 

صفحات  -

تاریخ انتشار 2012