Finite automata over algebraic structures: models and some methods of analysis
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SKOBELEV, Volodymyr, SKOBELEV, Volodymyr. Finite automata over algebraic structures: models and some methods of analysis. In: Computer Science Journal of Moldova, 2015, nr. 2(68), pp. 165-188. ISSN 1561-4042.
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Computer Science Journal of Moldova
Numărul 2(68) / 2015 / ISSN 1561-4042 /ISSNe 2587-4330

Finite automata over algebraic structures: models and some methods of analysis
CZU: 510.5+519.7+004

Pag. 165-188

Skobelev Volodymyr, Skobelev Volodymyr
 
Institute of Cybernetics, National Academy of Sciences of Ukraine
 
Disponibil în IBN: 20 noiembrie 2015


Rezumat

In this paper some results of research in two new trends of finite automata theory are presented. For understanding the value and the aim of these researches some short retrospective analysis of development of finite automata theory is given. The first trend deals with families of finite automata defined via recurrence relations on algebraic structures over finite rings. The problem of design of some algorithm that simulates with some accuracy any element of given family of automata is investigated. Some general scheme for design of families of hash functions defined by outputless automata is elaborated. Computational security of these families of hash functions is analyzed. Automata defined on varieties with some algebra are presented and their homomorphisms are characterized. Special case of these automata, namely automata on elliptic curves, are investigated in detail. The second trend deals with quantum automata. Languages accepted by some basic models of quantum automata under supposition that unitary operators associated with input alphabet commute each with the others are characterized.

Cuvinte-cheie
finite automata, varieties, simulation,

finite rings, hash functions, elliptic curves, quantum automata.