A Characterization of the Computational Power of Rule-based Visualization

Declarative visualization is a paradigm in which the process of visualization is treated as a mapping from some domain (typically a program) to an image. One means of declaring such mappings is through the use of rules which specify the relationship between the domain and the image. This paper examines the computational power of such rule-based mappings. Computational power is measure using three separate criteria. The first of these uses the Chomsky hierarchy, in which computational power is treated as string-acceptance; with this criterion we are able to show that certain rule-based models are equivalent in power to Turing machines. The second criterion is the evaluation of recursive functions, while the third is a more informal consideration of the abstractive capabilities of the mapping.