Fractal symbolic analysis

Fractal Symbolic Analysis for Program Transformations

Restructuring compilers use dependence analysis to prove that the meaning of a program is not changed by a transformation. A well-known limitation of dependence analysis is that it examines only the memory locations read and written by a statement, and does not assume any particular interpretation for the operations in that statement. Exploiting the semantics of these operations enables a wider...

Left to Right and vice versa: Applying Fractal Symbolic Analysis to Restructuring Linear Algebra Codes

We have recently developed a new program analysis strategy called fractal symbolic analysis that addresses some of limitations of techniques such as dependence analysis. In this paper, we show how fractal symbolic analysis can be used to convert between left-looking and right-looking versions of three kernels of central importance in computational science: Cholesky factorization, LU factorizati...

Building Predictive Models from Fractal Representations of Symbolic Sequences

We propose a novel approach for building finite memory predictive models similar in spirit to variable memory length Markov models (VLMMs). The models are constructed by first transforming the n-block structure of the training sequence into a spatial structure of points in a unit hypercube, such that the longer is the common suffix shared by any two n-blocks, the closer lie their point represen...

Fractal Behaviour Analysis

A fundamental problem of AI is that of how to simulate a particular kind of behaviour – that of intelligence. This paper describes an alternative approach to reproducing action systems by a geometric analysis of behaviour. If the behaviour to be reproduced has a particular character, a character identified by a self-affinity like that of fractal images, it may be possible to infer a program cap...

Evaluation of fractal dimensions for analysis of aggregate stability