Maximum subclasses in classes of linear automata over finite fields
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Anatoliy A. Chasovskikh
Abstract
The sets of all maximum subclasses in classes of linear automata over finite fields are found. An algorithm that decides completeness of finite subsets based on maximum subclasses is formulated.
Note: Originally published in Diskretnaya Matematika (2019) 31,№4, 88–101 (in Russian)
References
[1] Babin D. N., “Algorithm for completeness of systems of automaton functions with a complete Boolean part”, Intellektual’nye sistemy 7:1–4 (2003), 199–222 (in Russian).10.1515/156939203321669564Search in Google Scholar
[2] van der Waerden B. L., Algebra Frederick Ungar Publishing, New York, 1970.Search in Google Scholar
[3] Gill A., Linear Sequential Circuits. Analysis, Synthesis and Applications N.Y.: McGraw-Hill, 1966, 216 pp.Search in Google Scholar
[4] Kudryavtsev V. B., “On the cardinality of sets of precomplete sets of some functional systems connected with automata”, Problemy kibernetiki 1965,№13, 45–74 (in Russian)Search in Google Scholar
[5] Kudryavtsev V. B., Aleshin S. V., Podkolzin A. S., Introduction to automata theory M.: Nauka, 1985 (in Russian), 320 pp.Search in Google Scholar
[6] Lang S., Algebra Addison-Wesley Pub. Co., 1965, 508 pp.Search in Google Scholar
[7] Lidl R., Niederreiter H., Finite Fields Addison-Wesley Publ. Inc., 1983.Search in Google Scholar
[8] Chasovskikh A. A., “Completeness problem for the class of linear automata functions”, Discrete Math. Appl. 26:2 (2016), 89–104.10.1515/dma-2016-0007Search in Google Scholar
[9] Chasovskikh A. A., “Completeness conditions for linear p-automatic functions”, Intellektual’nye sistemy. Teoriya i prilozheniya 18:3 (2014), 203–252 (in Russian).Search in Google Scholar
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Articles in the same Issue
- Frontmatter
- Group polynomials over rings
- Maximum subclasses in classes of linear automata over finite fields
- Using binary operations to construct a transitive set of block transformations
- Perfect matchings and K1,p-restricted graphs
- On the waiting times to repeated hits of cells by particles for the polynomial allocation scheme
- Semibinomial conditionally nonlinear autoregressive models of discrete random sequences: probabilistic properties and statistical parameter estimation
Articles in the same Issue
- Frontmatter
- Group polynomials over rings
- Maximum subclasses in classes of linear automata over finite fields
- Using binary operations to construct a transitive set of block transformations
- Perfect matchings and K1,p-restricted graphs
- On the waiting times to repeated hits of cells by particles for the polynomial allocation scheme
- Semibinomial conditionally nonlinear autoregressive models of discrete random sequences: probabilistic properties and statistical parameter estimation
