Abstract
A logical analysis of string manipulation systems is presented that provides a unification of many formalisms and suggests a framework for the investigation of complex discrete dynamics. Namely, several characterizations of computational universality are given in terms of logical representability within models and theories; moreover, combinatorial schemata, as a formal counterpart of DNA basic recombinant mechanisms, are logically expressed. In this way a general definition of derivation systems is given to which many classical systems can be easily reduced, and where some regulation mechanisms can be naturally represented. As a further consequence, systematic methods are provided for translating derivation systems into monoidal theories. Finally, new possibilities of this logical approach are outlined in the formalization of molecule manipulation systems inspired by chemical and biochemical processes.
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