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 seems as a ordinary three-sorted algebraic constitution, that enables for a wealthy algebraic conception. in accordance with a common type 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 enables us to think about theoretical difficulties of databases.

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**Example text**

A homomorphic a Moore image of the Moore automaton may not be automaton. I n view o f the C o r o l l a r y the q u e s t i o n a r i s e s , when a homomorphic image o f the Moore automaton i s again a Moore automaton. 6.

L a l a * i l aoam 1 1 I I r i Similarly, a *(o-,,ffl )=a *(c ,d ). 2))=a«(c ,d ) = (according t o (2. 5) )=a »{

Denote t h i s automaton by Atm*(i/):r —* B). T —* B i s * surjective, i . e . T ~* B) i s a c y c l i c automaton w i t h generator element 1 ( u n i t element) from I * . "1 —* Fun(T,B). Remark. rjpr2 (by the d e f i n i t i o n means t h a t yi *x=y2 »x f o r a l l xel". I t i s e q u i v a l e n t o f the o p e r a t i o n •) t o t h a t - f o r every x e l holds (y x)^=(y x ) ^ . 6. Every reduced morphic to a certain automaton cyclic automaton equivalence. a(A,r,B) is iso- Atm(^:T — * B ) .