New PDF release: Algebraic Structures in Automata and Database Theory

By B. I. Plotkin

ISBN-10: 9810209363

ISBN-13: 9789810209360

The e-book 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 enables for a wealthy algebraic conception. in keeping with a basic 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 permits us to contemplate theoretical difficulties of databases.

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Additional resources for Algebraic Structures in Automata and Database Theory

Example text

Homomorphism i s a mathematical n o t i o n which r e f l e c t s the p h y s i c a l concept o f modeling. 3) o f the l a t t e r d e f i n i t i o n are one-to- one, u i s c a l l e d an isomorphism of automata. A homomorphism (isomor- phism) o f an automaton 3 i n t o i t s e l f i s c a l l e d an endomorphism (automorphism) o f an automaton. A b s o l u t e l y pure automata w i t h t h e i r homomorphisms form a category. Semigroup automata together w i t h t h e i r homomorphisms also form a s category.

Since (e, ip) (e, 0) = (e, iji), then the image right o f the semigroup T i n S(A,B) i s a semigroup o f the zeros. But by the c o n d i t i o n T i s not a semigroup o f the r i g h t zeros. Hence, f not cannot be a monomorphism and the automaton an exact one. In particular, the automaton Atm (A,D (A,r,B) i s i s also not exact. b) Let T be a semigroup w i t h a u n i t and (A,D be such a represent a t i o n t h a t the u n i t does not act i n A i d e n t i c a l l y . Then any automaton (A, T, B) extending t h i s r e p r e s e n t a t i o n cannot be take the element aeA left reduced.

An a b s o l u t e l y pure automaton (A,X,B) i s c a l l e d an exact if the associated mapping X —* S(A,B) i s i n j e c t i v e . B) i s an exact one, i f the homomorphism f:T ~* S(A,B) i s a monomorphism o f semigroups, i . e . d i f f e r e n t elements o f T correspond t o d i f f e r e n t elements o f S(A,B). The k e r n e l congruence p=Kerf of the semigroup T i s c a l l e d the k e r n e l o f the automaton r e p r e s e n t a t i o n , 16 or the kernel of the automaton 9 . An exact automaton (A,r/p,B) can be assigned t o each automaton 9=(A,r,B).

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Algebraic Structures in Automata and Database Theory by B. I. Plotkin

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