Search results for "Circuit minimization for Boolean functions"
showing 2 items of 2 documents
BMaD – A Boolean Matrix Decomposition Framework
2014
Boolean matrix decomposition is a method to obtain a compressed representation of a matrix with Boolean entries. We present a modular framework that unifies several Boolean matrix decomposition algorithms, and provide methods to evaluate their performance. The main advantages of the framework are its modular approach and hence the flexible combination of the steps of a Boolean matrix decomposition and the capability of handling missing values. The framework is licensed under the GPLv3 and can be downloaded freely at http://projects.informatik.uni-mainz.de/bmad.
Quantum Query Complexity of Boolean Functions with Small On-Sets
2008
The main objective of this paper is to show that the quantum query complexity Q(f) of an N-bit Boolean function f is bounded by a function of a simple and natural parameter, i.e., M = |{x|f(x) = 1}| or the size of f's on-set. We prove that: (i) For $poly(N)\le M\le 2^{N^d}$ for some constant 0 < d < 1, the upper bound of Q(f) is $O(\sqrt{N\log M / \log N})$. This bound is tight, namely there is a Boolean function f such that $Q(f) = \Omega(\sqrt{N\log M / \log N})$. (ii) For the same range of M, the (also tight) lower bound of Q(f) is $\Omega(\sqrt{N})$. (iii) The average value of Q(f) is bounded from above and below by $Q(f) = O(\log M +\sqrt{N})$ and $Q(f) = \Omega (\log M/\log N+ \sqrt{N…