Generalized de Bruijn graphs
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Fedor M. Malyshev
Abstract
We study the graphs of transitions between states of nonautonomous automata that provide, with independent equiprobable input signs, an equiprobable distribution on the set of all states in the minimum possible number of cycles, as is the case of the de Bruijn graphs corresponding to shift registers. It is proved that in the case of a binary input alphabet, there are at least 12r−33 pairwise nonisomorphic directed graphs with 2r vertices that have this property. All graphs of this type with 8 and 9 vertices are found.
Note: Originally published in Diskretnaya Matematika (2020) 32,№4, 52–88 (in Russian).
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© 2022 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Single diagnostic tests for inversion faults of gates in circuits over arbitrary bases
- Generalized de Bruijn graphs
- A family of asymptotically independent statistics in polynomial scheme containing the Pearson statistic
- Linear recurrent relations, power series distributions, and generalized allocation scheme
- Variance of the number of cycles of random A-permutation
- Multi-dimensional Kronecker sequences with a small number of gap lengths
Artikel in diesem Heft
- Frontmatter
- Single diagnostic tests for inversion faults of gates in circuits over arbitrary bases
- Generalized de Bruijn graphs
- A family of asymptotically independent statistics in polynomial scheme containing the Pearson statistic
- Linear recurrent relations, power series distributions, and generalized allocation scheme
- Variance of the number of cycles of random A-permutation
- Multi-dimensional Kronecker sequences with a small number of gap lengths
