Regular Expression Basics Regular expressions (regex) are an effective way of describing common patterns in strings. For example, all phone numbers in North America have 10 digits; this can be easily described by regular expressions: [0-9]{10}, which matches with 10 …
Definition of Pseudorandom Generators Two distributions \(X\) and \(Y\) over \(\{0,1\}^n\) are \((s, \epsilon)\)-indistinguishable if, for any circuit \(C\) of size at most \(s\), \[ \left| \Pr_X[C(X) = 1] – \Pr_Y[C(Y) = 1] \right| \leq \epsilon. \] A pseudorandom generator …
Fourier Transform Consider a function \(f\colon \{0,1\}^n \to \{-1, 1\}\) on \(n\) boolean variables. This can be viewed as a transform of a boolean function \(g\colon \{0,1\}^n \to \{0, 1\}\) by letting \(f(x) = (-1)^{g(x)}\). For \(\alpha \in\{0,1\}^n\), define the …
Fourier Analysis of Boolean Functions under Random Restriction Read more »
Selecting random records from a table is helpful when showing items with no preferences or testing different result sets. The following SQL defines a table holding images. Imagine that we wish to pick up 10 random rows from it. In …