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

Authors:
Matteo Cavaliere;Peter Leupold
Affiliations:
Department of Computer Science and Artificial Intelligence, University of Sevilla, Sevilla, Spain;Research Group in Mathematical Linguistics, Rovira i Virgili University, Tarragona, Spain
Venue:
MCU'04 Proceedings of the 4th international conference on Machines, Computations, and Universality
Year:
2004

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Abstract

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.