Quantum Finite Automata and Logic
View metadata, citation and similar papers at core.ac.uk brought to you by CORE provided by E-resource repository of the University of Latvia University of Latvia Ilze Dzelme-Berzin¸a¯ Quantum Finite Automata and Logic Doctoral Thesis Area: Computer Science Sub-Area: Mathematical Foundations of Computer Science Scientific Advisor: Dr. habil. math., Prof. Rusin¸š¯ Freivalds Riga 2010 Abstract The connection between the classical computation and mathematical logic has had a great impact in the computer science which is the main reason for the interest in the connection between the quantum computation and mathematical logic. The thesis studies a connection between quantum finite state automata and logic. The main research area is a quantum finite state automaton and its different notations (measure-once quantum finite state automaton, measure-many quantum finite state automaton, and Latvian quantum finite state automaton), more precisely, the languages accepted by the various models of the quantum finite state automaton and its connection to languages described by the different kinds of logic (first order, modular etc.). Additionally, a quantum finite state automaton over infinite words is introduced. The first part of the thesis is devoted to the connection between such quantum finite state automata as measure-once quantum finite state automata, measure-many quantum finite state automata, and Latvian quantum finite state automata and first order logic, modular logic, and generalized quantifiers - Lindström quantifier and group quantifier. For measure-once quantum finite state automata, we have characterized the language class accepted by measure-once quantum finite state automata in terms of logic using generalized quantifiers - Lindström quantifier and group quantifier, studied the relationship between the language class accepted by measure-once quantum finite state automata and the language class described by first order logic and modular logic.
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