Journal ArticleDOI
Kolmogorov Complexity and Deterministic Context-Free Languages
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This paper gives a counterexample to the original KC-DCF lemma and also provides a corrected version, which works on a superset of examples compared to traditional iteration and pumping lemmas.Abstract:
We deal with a criterion for deterministic context-free languages that was originally formulated by Li and Vitanyi [SIAM J. Comput., 24 (1995), pp. 398--410]. Their result---called the KC-DCF lemma---relates Kolmogorov complexity to pushdown automata and works on a superset of examples compared to traditional iteration and pumping lemmas. Sadly, their KC-DCF lemma has a flaw. In this paper, we give a counterexample to the original KC-DCF lemma and also provide a corrected version.read more
Citations
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Proceedings Article
One-Way Bounded-Error Probabilistic Pushdown Automata and Kolmogorov Complexity - (Preliminary Report).
TL;DR: It is proved that a well-known language—the set of palindromes—cannot be recognized by any bounded-error ppda; in other words, this language stays outside of BPCFL.
Book ChapterDOI
One-Way Bounded-Error Probabilistic Pushdown Automata and Kolmogorov Complexity
TL;DR: In this paper, it was shown that the set of palindromes cannot be recognized by any bounded-error pushdown automata with error probabilities less than 1/2.
Book ChapterDOI
A Structural Lemma for Deterministic Context-Free Languages
TL;DR: The structural lemma allows not only to prove that a language is not a DCFL, but discloses the structure of DCFLs Myhill-Nerode classes.
Book ChapterDOI
Kolmogorov Complexity Descriptions of the Exquisite Behaviors of Advised Deterministic Pushdown Automata
Journal ArticleDOI
A pumping lemma for regular closure of prefix-free languages
TL;DR: In this article , a pumping lemma for ΓREG(PFL) was given, which enables us to prove that some prefix-free languages do not belong to PFL.
References
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Book
Introduction to formal language theory
TL;DR: This volume intended to serve as a text for upper undergraduate and graduate level students and special emphasis is given to the role of algebraic techniques in formal language theory through a chapter devoted to the fixed point approach to the analysis of context-free languages.
An introduction to Kolmogorov complexity and its applications
Ming Li,Paul M. B. Vitányi +1 more
TL;DR: The Journal of Symbolic Logic as discussed by the authors presents a thorough treatment of the subject with a wide range of illustrative applications, such as the randomness of finite objects or infinite sequences, Martin-Loef tests for randomness, information theory, computational learning theory, the complexity of algorithms, and thermodynamics of computing.
Journal ArticleDOI
A New Approach to Formal Language Theory by Kolmogorov Complexity
Ming Li,Paul M. B. Vitányi +1 more
TL;DR: The authors presented a new approach to formal language theory using Kolmogorov complexity, which is also successful at the high end of the Chomsky hierarchy, since one can quantify nonrecursiveness in terms of KCC.