Language of Lattice-Valued General Orthomodular Automata
Subject Areas : International Journal of Industrial Mathematics
Khadijeh Abolpour
1
*
,
Marzie shamsizadeh
2
1 - Department of Mathematics, Shiraz Branch, Islamic Azad University, Shiraz, Iran
2 - Department of Mathematics and Statistics, Faculty of Energy and Data Science, Behbahan Khatam Alanbia University of Technology, Behbahan, Iran
Keywords: Quantum logic, Orthomodular lattice, General fuzzy automata, Kleene theorem, Pumping lemma,
Abstract :
A new theory of computation based on quantum logic is being developed as a foundational framework for quantum computation. The idea of quantum computation emerged from exploring the relationship between physics and computation, with the initial focus on understanding the thermodynamics associated with classical computation. This research represents one of the initial efforts to explore this innovative theory. In this study, quantum logic is identified as an orthomodular lattice-valued logic. The primary objective is to establish a theory of general fuzzy automata grounded in this logic, employing a semantical analysis approach. As part of this work, concepts such as lattice-valued general orthomodular automata and regular languages have been introduced, along with new ideas related to orthomodular lattice-valued regular expressions. Additionally, the Kleene theorem has been characterized within the context of quantum logic, illustrating the equivalence between general fuzzy automata and regular expressions. Furthermore, an orthomodular lattice-valued variant of the pumping lemma has also been formulated.
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