Cota superior para la longitud de secuencias malas en el orden mayorante con aplicación a complejidad de problemas de decisión en autómatas sobre árboles

• Autores: Senno, Gabriel Ignacio
• Año de publicación: 2012
• Idioma: inglés
• Tipo de recurso: tesis de grado
• Colaborador/a o director/a de tesis: Figueira, Santiago Daniel
• Materia: WELL QUASI ORDER; MAJORING ORDERING; MULTISET ORDERING; TREE AUTOMATA; FAST GROWING HIERARCHY
• Institución: Universidad Nacional de Buenos Aires. Facultad de Ciencias Exactas y Naturales

Well quasi-orders (wqo’s) are an important mathematical tool for proving termination of many algorithms. Under some assumptions upper bounds for the computational complexity of such algorithms can be extracted by analyzing the length of controlled bad sequences. We obtain tight upper bounds, in terms of the Fast Growing Hierarchy, for the length of controlled decreasing sequences of multisets over the natural multiset ordering. Then we study the majoring wqo ≤maj of sets of tuples, which informally states that A ≤maj B iff every element of A is majorized by an element of B. We linearize this wqo into the multiset wellorder, to obtain an upper bound for the length of controlled ≤maj-bad sequences. We finally apply this result to upper-bound the computational complexity of the emptiness problem for ATRA, a class of automata over data trees.
Fil: Senno, Gabriel Ignacio. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina.