Response curves of deterministic and probabilistic cellular automata in one and two dimensions

One of the most important problems in the theory of cellular automata (CA) is determining the proportion of cells in a specific state after a given number of time iterations. We approach this problem using patterns in preimage sets - that is, the set of blocks which iterate to the desired output. This allows us to construct a response curve - a relationship between the proportion of cells in state 1 after niterations as a function of the initial proportion. We derive response curve formulae for many two-dimensional deterministic CA rules with L-neighbourhood. For all remaining rules, we find experimental response curves. We also use preimage sets to classify surjective rules. In the last part of the thesis, we consider a special class of one-dimensional probabilistic CA rules. We find response surface formula for these rules and experimental response surfaces for all remaining rules.

Decoding algorithms using side-effect machines

Bioinformatics applies computers to problems in molecular biology. Previous research has not addressed edit metric decoders. Decoders for quaternary edit metric codes are finding use in bioinformatics problems with applications to DNA. By using side effect machines we hope to be able to provide efficient decoding algorithms for this open problem. Two ideas for decoding algorithms are presented and examined. Both decoders use Side Effect Machines(SEMs) which are generalizations of finite state automata. Single Classifier Machines(SCMs) use a single side effect machine to classify all words within a code. Locking Side Effect Machines(LSEMs) use multiple side effect machines to create a tree structure of subclassification. The goal is to examine these techniques and provide new decoders for existing codes. Presented are ideas for best practices for the creation of these two types of new edit metric decoders.