I would like to thank my advisor and friend Prof. Dr. Caetano Traina Jr., who believed in me from the beginning when invited me to do undergraduate research. He afforded me opportunities and challenges, support and encouragement at all time, and mainly trust. My thanks to my French advisor, Prof. Dr. Richard Chbeir, who also contributed to guide my work. My special thanks to my dear husband Leandro, for always being there, for sharing happy moments and encouraging me to overcome difficult times, for his comprehension during my absences in countless weekends and holidays that I had to work, for his sweet words that make everything seems so much easier. I would like to thank my parents, José Maria and Mayra, my grandmother Ladice and all my family that is very large and I can not mention one by one, for their unconditional love, support and encouragement dedicated throughout my life, for their comprehension during my absences in holidays and family gatherings, for their hug and cheer all the time. I also thank my brothers José Maria Jr. and José Guilherme, my sister-in-law Josélia, my brother-in-law Rudinei, my nephews João Pedro and Diego, and my parents-in-law Maria Helena and Celso for their attention, encouragement words and for always being around when I needed. My sincere thanks to my sister-in-law Elaine for helping and teaching me many things throughout my academic life. My special thanks to my grandmother and heroine Carminda (in memoriam) and to my aunt and godmother Dama (in memoriam) for their love and support, for their life examples, for their unconditionally encouragement dedicated throughout my life, for hugging and cheering me all the time. My gratitude to Profa. Agma Traina at ICMC-USP for her time and effort on my thesis, for her collaborative work, ideas, words of encouragement and for her affection demonstrated always so kind. I also thanks Profa. Ires Dias for the collaborative work, time and effort invested with the algebra. My grateful to Profa. Sandra de Amo and Prof. Renato Fileto for their contribution to my work. I dedicate my sincere thanks to my friends and colleagues of the GBdI-USP in São Carlos-SP-Brazil, especially I am grateful to Prof. Junior, Robson, Carolina, Letrícia, Jaqueline, Willian, Lucio, Sérgio and Daniel C. for their important collaboration in the lab and meetings. I also thanks my colleagues of the Le2i-uB in Dijon-France. I am grateful to my friends Marcela Ribeiro, Luciana Romani, Fekade Getahum and Elie Raad for their contributions to my work and for incentive words in moments of despair and anguish. My thanks to Laura, Glaucia, Ana Paula, Lhais and Carolina for helping me with bureaucracies. I also thank the Instituto de Ciências Matemáticas e de Computação of USP in São Carlos-SP-Brazil and Université de Bourgogne in Dijon-France for their academic structures that became possible the development of this cotutlle work. Finally, I acknowledge the funding agencies FAPESP and CAPES for the financial support during this doctorate. Additionally, I thanks the funding ag...