NON-DETERMINISTIC AUTOMATA AND EFFECTIVE LANGUAGES.
IOWA UNIV IOWA CITY DEPT OF MATHEMATICS
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In the dissertation, the concept of a finite automation is extended to a non-deterministic automaton over any arbitrary semigroup. The languages recognized by these non-deterministic automata are also characterized by regular expressions. Then a specific subclass of these automata is defined as deterministic automata which are characterized by congruences of finite index on the semigroup. The closure properties of these languages are then examined. In order to relate the languages recognized by non-deterministic automata to computable sets or formal languages, a specific type of computable semigroup called sigma-effective semigroup is introduced. Then associated classes of effective languages are defined. It is shown that for any sigma-effective semigroup one can constructively find another which is finitely generated such that the two effective languages are the same.
- Computer Programming and Software