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I wish to thank many people. Their cooperation enabled me to complete this thesis and my research. First, my supervisor Prof. Nobuyoshi Asai. I greatly appreciate my supervisor Prof. Nobuyoshi Asai for help, support, advice, and valuable discussions. Secondly, I thank all members of the Mathematical Foundation of Computer Science Laboratory, Yoshikatsu Matsumoto, Wataru Ishikawa, Toshiyuki Oowada, Daisuke Takahashi. They gave me some good ideas, advice, and objective opinions. Finally, I thank Prof. Yasuhiko Ikebe who gave us a wonderful theme for this research[15]. Thank you all very much.