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1995•SIAM Journal on ComputingRequires access

A New Approach to Formal Language Theory by Kolmogorov Complexity

Ming Li, Paul M. B. Vitanyi

Open publisher page 25 citations

Abstract

We present a new approach to formal language theory by using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate deterministic context-free languages and nondeterministic context-free languages. The use of the “incompressibility arguments” is illustrated by many examples. The approach is also successful at the high end of the Chomsky hierarchy since one can quantify nonrecursiveness in terms of Kolmogorov complexity.

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What this paper is about

We present a new approach to formal language theory by using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate deterministic context-free languages and nondeterministic context-free languages. The use of the “incompressibility arguments” is illustrated by many examples. The approach is also successful at the high end of the Chomsky hierarchy since one can quantify nonrecursiveness in terms of Kolmogorov complexity.

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Available abstract

We present a new approach to formal language theory by using Kolmogorov complexity. The main results presented here are an alternative for pumping lemma(s), a new characterization for regular languages, and a new method to separate deterministic context-free languages and nondeterministic context-free languages. The use of the “incompressibility arguments” is illustrated by many examples. The approach is also successful at the high end of the Chomsky hierarchy since one can quantify nonrecursiveness in terms of Kolmogorov complexity.

Key concepts: Formal language, Chomsky hierarchy, Kolmogorov complexity, Nondeterministic algorithm, Regular language, Computer science, Context-free language, Hierarchy

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