A pumping lemma for deterministic context-free languages

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Abstract

In this paper, we introduce a new pumping lemma and a new iteration theorem for deterministic context-free languages (DCFLs). As application of the lemma, several languages are shown not to be deterministic context-free by using this lemma. An iteration theorem for DCFLs has already been introduced by Harrison in [3]. However, the result presented in this paper is different from his. Instead of considering the pumping property of individual words, we consider the pumping property of pairs of words.

The latter approach seems more natural to the DCFLs (LR(1) languages). The pumping lemma introduced in this paper also appears to be easier to understand and use. We conjecture that there exist languages that can be shown not to be DCFLs by this new result but cannot be shown by the existing one.

In Section 1, we introduce the basic notations used in this paper. In Section 2, we state our pumping lemma (without a proof) and show two applications of the lemma. In Section 3, a left-part theorem for LR (k) grammars is introduced, which is crucial to the proof of the pumping lemma and interesting on its own right. In the last section, we prove the lemma and extend it to an iteration theorem.

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