Algebraic Characterization of IF-Automata

In the present work, we have introduced the concept of layers of IF-automaton, provide the characterization of algebraic concepts of an IF-automaton from its layer point of view, and investigate relationship between IF-automata and upper semilattices. We also confer a decomposition of an IF-automaton and investigate a method of formation of an IF-automaton for a given finite poset. Interestingly, we have demonstrated that there exists an isomorphism between an upper semilattice and the poset of class of subautomata of an IF-automaton.