A generalization of Shannon function
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Nikolay P. Redkin
Abstract
When investigating the complexity of implementing Boolean functions, it is usually assumed that the basis inwhich the schemes are constructed and the measure of the complexity of the schemes are known. For them, the Shannon function is introduced, which associates with each Boolean function the least complexity of implementing this function in the considered basis. In this paper we propose a generalization of such a Shannon function in the form of an upper bound that is taken over all functionally complete bases. This generalization gives an idea of the complexity of implementing Boolean functions in the “worst” bases for them. The conceptual content of the proposed generalization is demonstrated by the example of a conjunction.
Originally published in Diskretnaya Matematika (2017) 29, №2, 70–83 (in Russian).
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Articles in the same Issue
- Frontmatter
- A subcritical decomposable branching process in a mixed environment
- Limit theorems for bounded branching processes
- On coincidences of tuples in a q-ary tree with random labels of vertices
- A generalization of Shannon function
- Reduced critical Bellman–Harris branching processes for small populations
- Estimates of the mean size of the subset image under composition of random mappings
- Necessary conditions for power commuting in finite-dimensional algebras over a field
Articles in the same Issue
- Frontmatter
- A subcritical decomposable branching process in a mixed environment
- Limit theorems for bounded branching processes
- On coincidences of tuples in a q-ary tree with random labels of vertices
- A generalization of Shannon function
- Reduced critical Bellman–Harris branching processes for small populations
- Estimates of the mean size of the subset image under composition of random mappings
- Necessary conditions for power commuting in finite-dimensional algebras over a field
