@article {de2011complex, title = {On the complex behavior of simple tag systems — An experimental approach}, journal = {Theoretical Computer Science}, volume = {412}, number = {1}, year = {2011}, pages = {97{\textendash}112}, abstract = {

It is a well-know fact that apparently simple systems can give rise to complex behavior. But why exactly does a given system behave in a complex manner? There are two main approaches to tackle this and other related questions. One can take on a more theoretical approach or start from a more experimental study of the behavior of such systems with the help of the computer. In this paper, the experimental approach will be applied to very small tag systems. After a discussion of some of the main theoretical results on tag systems, several results from a computer-assisted and experimental study on tag systems will be analyzed. Special attention will be given to the well-known example Post provided and studied with only 2 symbols and a deletion number v = 3. These results will be combined with some theoretical results on tag systems in order to gain more insight into the computational power of simple tag systems.

}, author = {De Mol, Liesbeth} } @article {340414, title = {Closing the circle: An analysis of {E}mil {P}ost{\textquoteright}s early work}, journal = {Bulletin of symbolic logic}, volume = {12}, number = {2}, year = {2006}, pages = {267{\textendash}289}, abstract = {

In 1931 Kurt G{\"o}del published his incompleteness results, and some years later Church and Turing showed that the decision problem for certain systems of symbolic logic has a negative solution. However, already in 1921 the young logician Emil Post worked on similar problems which resulted in what he called an “anticipation” of these results. For several reasons though he did not submit these results to a journal until 1941. This failure ‘to be the first’, did not discourage him: his contributions to mathematical logic and its foundations should not be underestimated. It is the purpose of this article to show that an interest in the early work of Emil Post should be motivated not only by this historical fact, but also by the fact that Post’s approach and method differs substantially from those offered by G{\"o}del, Turing and Church. In this paper it will be shown how this method evolved in his early work and how it finally led him to his results.

}, issn = {1079-8986}, author = {De Mol, Liesbeth} } @conference {383110, title = {Computer Generated Images as Mathematical Tools}, booktitle = {Proceedings of the 7th International Conference and Exhibition on Generative Art}, year = {2004}, abstract = {

Since the commercialisation of the computer, it became possible to visualise certain aspects of mathematics that were not possible to visualise before because of the complexity or the size of the datasets involved. Some of these computer generated images even have become the icons of certain mathematical theories like for example fractal geometry. One of the advantages of these visualisations is the fact that in using them, certain properties that involve complexity can be immediately shown. This possibility will be discussed through experiments done by the author.

}, author = {De Mol, Liesbeth} }