A New Approach to Formal Language Theory by Kolmogorov Complexity (Preliminary Version)

We introduce Kolmogorov complexity as a new technique in Formal Language Theory. We give an alternative for pumping lemma(s) and a new characterization for regular languages. For the separation of deterministic contextfree languages and contextfree languages no pumping lemmas or any other general method was known. We give a first general technique to separate these classes, and illustrate its use on four examples previously requiring labourous ad hoc methods. The approach is also successful at the high end of the Chomsky hierarchy since one can quantify nonrecursiveness in terms of Kolmogorov complexity. We also give a new proof, using Kolmogorov complexity, of Yao and Rivest's result that k + 1 heads are better than k heads.

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