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- Title
Finite automata and numbers.
- Authors
Aleshin, Stanislav V.; Panteleev, Pavel A.
- Abstract
We study finite automata representations of numerical rings. Such representations correspond to the class of linear p-adic automata that compute homogeneous linear functions with rational coefficients in the ring of p-adic integers. Finite automata act both as ring elements and as operations. We also study properties of transition diagrams of automata that compute a function f( x)= cx of one variable. In particular we obtain precise values for the number of states of such automata and show that for c > 0 transition diagrams are self-dual (this property generalises self-duality of Boolean functions). We also obtain the criterion for an automaton computing a function f( x)= cx to be a permutation automaton, and fully describe groups that are transition semigroups of such automata.
- Subjects
FINITE state machines; NUMBER theory; COEFFICIENTS (Statistics); DUALITY theory (Mathematics); BOOLEAN functions; P-adic numbers; RING theory
- Publication
Discrete Mathematics & Applications, 2016, Vol 26, Issue 3, p131
- ISSN
0924-9265
- Publication type
Article
- DOI
10.1515/dma-2016-0011