Abstract
The purpose of this work is to introduce and study the concept of minimal deterministic automaton with IF-outputs which realizes the given IF-language. Among two methods for construction of such automaton pre- sented here, one is based on Myhill-Nerode's theory while the other is based on derivatives of the given IF-language. Meanwhile, the categories of deter- ministic automata with IF-outputs and IF-languages alongwith a functorial relationship between them are introduced
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