Bounds for the average-case complexity of monotone Boolean functions
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Aleksandr V. Chashkin
Abstract
We consider average-case complexity of computing monotone Boolean functions by straight-line programs with a conditional stop over the basis of all Boolean functions of at most two variables. For the set of all n-ary monotone Boolean functions new Shannon-type upper and lower bounds for the average-case complexity as n → ∞ are established.
Originally published in Diskretnaya Matematika (2016) 28, №2, 146-153 (in Russian).
Funding source: Russian Foundation for Basic Research
Award Identifier / Grant number: 14-01-00598
Funding statement: This work was supported by the Russian Foundation for Basic Research, project no. 14-01-00598.
References
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[3] Chashkin A. V., “On the average time for the computation of the values of Boolean functions”, J. Applied and Industrial Mathematics, 4:1 (1997), 60-78 (in Russian).Suche in Google Scholar
[4] Chashkin A. V., “On the average time for computing Boolean operators”, J. Applied and Industrial Mathematics, 5:1 (1998), 88-103 (in Russian).10.1016/S0166-218X(02)00293-7Suche in Google Scholar
© 2017 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Bounds for the average-case complexity of monotone Boolean functions
- Modular algorithm for reducing matrices to the Smith normal form
- Distribution of the extreme values of the number of ones in Boolean analogues of the Pascal triangle
- Application of Hadamard product to some combinatorial and probabilistic problems
- Cardinality of subsets of the residue group with nonunit differences of elements
Artikel in diesem Heft
- Frontmatter
- Bounds for the average-case complexity of monotone Boolean functions
- Modular algorithm for reducing matrices to the Smith normal form
- Distribution of the extreme values of the number of ones in Boolean analogues of the Pascal triangle
- Application of Hadamard product to some combinatorial and probabilistic problems
- Cardinality of subsets of the residue group with nonunit differences of elements
