By B. I. Plotkin

The publication is dedicated to the research of algebraic constitution. The emphasis is at the algebraic nature of actual automation, which appears to be like as a average three-sorted algebraic constitution, that permits for a wealthy algebraic idea. in accordance with a basic classification place, fuzzy and stochastic automata are outlined. the ultimate bankruptcy is dedicated to a database automata version. Database is outlined as an algebraic constitution and this permits us to contemplate theoretical difficulties of databases.

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The problem o f c o n s t r u c t i o n o f the exact automaton 3 / X p a l s o has p r a c t i c a l argumentation and f o r f i n i t e automata there e x i s t s t h e corresponding simple a l g o r i t h m . The automaton (A,r,B) and automaton (A',r,B) are c a l l e d e q u i v a l e n t i n states, mata are isomorphic c a l l e d equivalent i n s t a t e s . B) and (A, r",B) are i f the corresponding exact automata are isomorphic i n i n p u t s . 3. If there exists an epimorphism tp=(

3'=(A',r,B), then 1 A equivalent the automata in states.

1) On the exactness the of the Moore automaton. r —> S(A,B) i s t r i v i a l . T —> S^. R e a l l y , Kerf=KeranKer/3 where 6 i s a mapping o f T i n t o Fun(A, B) corresponding t o t h e g i v e n automaton. However, i f KeracKerB, then Kerf=Kera and the exactness o f the automaton 3 i s e q u i v a l e n t t o t h e exactness o f the r e p r e s e n t a t i o n ( A , D . By the d e f i n i t i o n o f Moore automata the i n c l u s i o n KeracKerB holds. Therefore, the exactness o f the Moore automaton (A,r,B) i s e q u i v a l e n t t o the exactness o f the represent a t i o n (A, T ) .

This d e f i n i t i o n i s correct, Suppose that i n t h e form (a, b r =(acr, aip) i . e . i t does n o t depend on t h e manner o f the r e p r e s e n t a t i o n o f the element (a,b) i n t h e form l e t (a,b) = (a

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