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1	Solving Nested Recursions with Trees Isgur, Abraham 19 June 2014 (has links) This thesis concerns the use of labelled infinite trees to solve families of nested recursions of the form $R(n)=\sum_{i=1}^kR(n-a_i-\sum_{j=1}^{p_i}R(n-b_{ij}))+w$, where $a_i$ is a nonnegative integer, $w$ is any integer, and $b_{ij},k,$ and $p_i$ are natural numbers. We show that the solutions to many families of such nested recursions have an intriguing combinatorial interpretation, namely, they count nodes on the bottom level of labelled infinite trees that correspond to the recursion. Furthermore, we show how the parameters defining these recursion families relate in a natural way to specific structural properties of the corresponding tree families. We introduce a general tree ``pruning" methodology that we use to establish all the required tree-sequence correspondences. Nested Recursion Labelled Tree Frequency Sequence Slowly Growing Sequence Enumerative Combinatorics 0405
2	Solving Nested Recursions with Trees Isgur, Abraham 19 June 2014 (has links) This thesis concerns the use of labelled infinite trees to solve families of nested recursions of the form $R(n)=\sum_{i=1}^kR(n-a_i-\sum_{j=1}^{p_i}R(n-b_{ij}))+w$, where $a_i$ is a nonnegative integer, $w$ is any integer, and $b_{ij},k,$ and $p_i$ are natural numbers. We show that the solutions to many families of such nested recursions have an intriguing combinatorial interpretation, namely, they count nodes on the bottom level of labelled infinite trees that correspond to the recursion. Furthermore, we show how the parameters defining these recursion families relate in a natural way to specific structural properties of the corresponding tree families. We introduce a general tree ``pruning" methodology that we use to establish all the required tree-sequence correspondences. Nested Recursion Labelled Tree Frequency Sequence Slowly Growing Sequence Enumerative Combinatorics 0405
3	Elementos de Semántica Denotacional de Lenguajes de Programación con Datos Borrosos Sánchez Álvarez, Daniel 01 October 1999 (has links) A fin de diseñar e implementar lenguajes de programación que tengan en cuenta el paradigma borroso modificaremos el lambda cálculo clásico, adjuntando a cada término un grado, y redefiniendo la beta-reducción, obteniendo que para que el nuevo cálculo verifique la propiedad de Church-Rosser la transmisión de los grados debe hacerse por medio de una función que sea una t-norma o s-conorma. Utilizando esta nueva herramienta diseñamos un lenguaje no determinista que satisface los requerimientos de la programación con datos borrosos. / With the aim of designing and implementing programming languages that take into account the fuzzy paradigm we will modify the classical lambda calculus by adding a degree to each term and by redefining the b-reduction. Thus, for the new calculus to verify the Church-Rosser property, the degree computed with can be made through a function that is a t-norm or an s-conorm. With this new tool we design a nondeterminist language that satisfies fuzzy dataprogramming requirements, and an example of its behaviour is shown. trapezoidal numbers Church numbers numerical system fuzzy numbers powerdomain directed sets fuzzy sets fuzzy boolean denotational semantics labelled tree s-conorma t-norma separabilidad sustitución reducción de Church-Rosser powerdomain número trapezoidal número de Church número borroso normalización ideal principal extensión cilíndrica dominio potencia conjunto dirigido conjunto borroso semántica denotacional booleano borroso árbol etiquetado Church-Rosser property abstract syntax guarded command substitutions reductions linguistic values linguistic variables t-norm s-conorm 621.3 68

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