Completeness problem for the class of linear automata functions
-
Anatoliy A. Chasovskikh
Abstract
We consider the classes of linear automata functions over finite fields with composition (superposition and feedback) operation and describe an algorithm that decides whether a finite set of functions from such class is complete. Thus we generalize the result that was known for the case of linear automata functions over prime finite fields.
Originally published in Diskretnaya Matematika (2015)27, No2, 134–151 (in Russian).
References
[1] Waerden B.L. van der, Algebra, transl. from German, Nauka, Moscow, 1976 (in Russian), 648 pp.Suche in Google Scholar
[2] Gill A., Linear sequential machines, transl. from English, Nauka, Moscow, 1974 (in Russian), 288 pp.Suche in Google Scholar
[3] Zariski O.,, Samuel P., Commutative Algebra, transl. from English, IL, Moscow, 1963 (in Russian), 373 pp.10.1007/978-3-662-29244-0Suche in Google Scholar
[4] Kudryavtsev V.B., Aleshin S.V., Podkolzin A.S., Introduction to automata theory, Nauka, Moscow, 1985 (in Russian), 320 pp.Suche in Google Scholar
[5] Lang S., Algebra, 3”, Addison-Wesley, 1993.Suche in Google Scholar
[6] Lidl R., Niederreiter H., “Finite fields”, Encyclopedia of Mathematics and its Applications,20, Addison-Wesley, 1987, 755 pp.Suche in Google Scholar
[7] Chasovskikh A.A., “Conditions of completeness linearly-p-automatic functions”, Int. Sys.,18 :3 (2014), 203–252 (in Russian). 104 [bar.two] Anatoliy A. Chasovskikh, Completeness problem for the class of linear automata functionsSuche in Google Scholar
[8] Lau D., Function Algebras on Finite Sets. A Basic Course on Many-Valued Logic and Clone Theory, Springer, Rostok, 2006, 668 pp.Suche in Google Scholar
[9] Szendrei Á., “On closed classes of quasilinear functions”, Chechoslovak Math. J.,30 :3 (1980), 498–509.10.21136/CMJ.1980.101699Suche in Google Scholar
2016 Walter de Gruyter GmbH, Berlin/Boston
Artikel in diesem Heft
- Frontmatter
- Article
- Functional limit theorems for the decomposable branching process with two types of particles
- Article
- Completeness problem for the class of linear automata functions
- Article
- Estimates of accuracy of the Poisson approximation for the distribution of number of runs of long string repetitions in a Markov chain
- Article
- Complexity of systems of functions of Boolean algebra and systems of functions of three-valued logic in classes of polarized polynomial forms
- Article
- A Markov chain with number-theoretic limit distribution
Artikel in diesem Heft
- Frontmatter
- Article
- Functional limit theorems for the decomposable branching process with two types of particles
- Article
- Completeness problem for the class of linear automata functions
- Article
- Estimates of accuracy of the Poisson approximation for the distribution of number of runs of long string repetitions in a Markov chain
- Article
- Complexity of systems of functions of Boolean algebra and systems of functions of three-valued logic in classes of polarized polynomial forms
- Article
- A Markov chain with number-theoretic limit distribution
