Evolution and observation: A non-standard way to accept formal languages

It is a very common procedure in biology to observe the progress of an experiment and regard the result of this observation as the final outcome. Inspired by this, a new approach for generating formal languages, called evolution/observation, has been introduced [6]. In the current work we consider evolution/observation as a new strategy also for accepting languages: a word is accepted, if the (observed) evolution of a certain system starting from this input follows a regular pattern. We obtain the following result: checking if the (observed) evolution of a context-free system follows a regular pattern is enough to accept every recursively enumerable languages. On the other hand, if we observe the evolution of systems using very simple rules (of the kind a -> b), then it is possible to accept exactly the class of context-sensitive languages.