Elizabeth Goode

Recognizing splicing languages: Syntactic monoids and simultaneous pumping

We use syntactic monoid methods, together with an enhanced pumping lemma, to investigate the structure of splicing languages. We obtain an algorithm for deciding whether a regular language is a reflexive splicing language, but the general question remains open.

Splicing to the Limit

We consider the result of a wet splicing procedure after the reaction has run to its completion, or limit, and we try to describe the molecules that will be present at this final stage. In language theoretic terms the splicing procedure is modeled as an H system, and the molecules that we want to consider correspond to a subset of the splicing language which we call the limit language. We give a number of examples, including one based on differential equations, and we propose a definition for the limit language. With this definition we prove that a language is regular if and only if it is the limit language of a reflexive and symmetric splicing system.

Semi-simple splicing systems

Generalizing a notion introduced by Păun and his coworkers, we introduce semi-simple splicing systems, in which all splicing rules have the form (a, 1; b,1) where a and b are single symbols. We find a simple graph representation of these systems, and from this representation we show that semi-simple splicing languages are reflexive splicing languages, that they contain constants, and that they are, in fact, strictly locally testable.

Splicing Systems: Regularity and Below

The motivation for the development of splicing theory is recalled. Attention is restricted to finite splicing systems, which are those having only finitely many rules and finitely many initial strings. Languages generated by such systems are necessarily regular, but not all regular languages can be so generated. The splicing systems that arose originally, as models of enzymatic actions, have two special properties called reflexivity and symmetry. We announce the Pixton-Goode procedure for deciding whether a given regular language can be generated by a finite reflexive splicing system. Although the correctness of the algorithm is not demonstrated here, two propositions that serve as major tools in the demonstration are stated. One of these is a powerful pumping lemma. The concept of the syntactic monoid of a language provides sharp conceptual clarity in this area. We believe that there may be yet unrealized results to be found that interweave splicing theory with subclasses of the class of regular languages and we invite others to join in these investigations.

DNA Implementation of a Royal Road Fitness Evaluation

A model for DNA implementation of Royal Road evolutionary computations is presented. An encoding for a Royal Road problem is presented. Experimental results utilizing 2-d denaturing gradient gel electrophoresis (2-d DGGE) and polyacrylamide gel electrophoresis (PAGE) for separation by fitness in this sample Royal Road problem are shown. Suggestions for possible use of the MutS and MutY proteins as tools for separation by fitness are given. Plans for future experiments and implementation are discussed.

DNA Splicing Systems

DNA splicing in the test tube may generate DNA molecules other than well-formed ones having two blunt ends. We introduce an example splicing system that generates all possible molecular types. We use differential equations to model the system, and Mathematica to simulate its dynamics. We find that most simulation results match our predictions, and acknowledge that a more comprehensive program is needed for further investigations. This is the first model and simulation of which we are aware that specifically treats the fact that several molecular types in addition to well-formed molecules may be present in a splicing system, even at equilibrium.