Artikel
Lizenziert
Nicht lizenziert
Erfordert eine Authentifizierung
On the complexity of Boolean functions with small number of ones
-
N. P. Redkin
Veröffentlicht/Copyright:
1. Oktober 2004
We consider the class of Boolean functions Fn,k consisting of all functions in n variables such that each of them takes value one exactly for k tuples of variables. We obtain linear in n estimates of the complexity of realisation of functions in Fn,k by circuits of functional elements over the basis containing all Boolean functions in two variables except the linear functions x ⊕ y and x ⊕ y ⊕ 1. It follows from these estimates that for small k, for example, for k < ln n, the well-known Finikov method provides asymptotically minimal circuits for all functions of Fn,k. In some cases, the known lower bounds for complexity of circuits give a possibility to prove the minimality of the corresponding circuits.
Published Online: 2004-10-01
Published in Print: 2004-10-01
Copyright 2004, Walter de Gruyter
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Sie haben derzeit keinen Zugang zu diesem Inhalt.
Artikel in diesem Heft
- Analysis of randomised rounding for integer programs
- Homomorphic relations of algebras with a scheme of operators
- On the connection between the eigen-vectors of weighted graphs and their subgraphs
- The asymptotic behaviour of the complexity of the interval search on the Boolean cube in the class of balanced trees
- Properties of systems of defining relations for automata
- Random free trees and forests with constraints on multiplicities of vertices
- On the complexity of Boolean functions with small number of ones
- A linear in memory non-exhaustive algorithm to solve a two-dimensional interval search problem
Artikel in diesem Heft
- Analysis of randomised rounding for integer programs
- Homomorphic relations of algebras with a scheme of operators
- On the connection between the eigen-vectors of weighted graphs and their subgraphs
- The asymptotic behaviour of the complexity of the interval search on the Boolean cube in the class of balanced trees
- Properties of systems of defining relations for automata
- Random free trees and forests with constraints on multiplicities of vertices
- On the complexity of Boolean functions with small number of ones
- A linear in memory non-exhaustive algorithm to solve a two-dimensional interval search problem
