Equivalence between an [formula omitted]-valued GOA with ε-moves and its ε-reduction

Abstract

The present study aims to develop the notion of L-valued general orthomodular automata (L-valued GOA) to a new one which is known as “L-valued GOA with ε-moves”. Subsequently, a clear relationship is attained between the language accepted by an L-valued GOA with ε-moves and the language accepted by ε-reduction. Moreover, it is demonstrated that certain commutativity which exists between basic actions of the automaton implies the equivalence between an automaton with ε-moves and its ε-reduction. Also, it is shown that the predicate commutative regularity is preserved by the Kleene closure and that consequently both the predicate regularity and commutative regularity are preserved by the pre-image of a homomorphism between the two languages. Finally, the quantum subset construction of L-valued GOA is presented as L-valued deterministic GOA (L-valued DGOA) and then the equivalence between L-valued GOA and L-valued DGOA is demonstrated. We further establish pumping lemma in the frame of quantum logic. To clarify the notions and the results obtained in this study, some examples are also submitted.