Affiliation:
1. Department of Mathematics and Computer Science, St. Petersburg State University, 14th Line V. O., 29, Saint Petersburg 199178, Russia
Abstract
This paper establishes an analogue of Greibach’s hardest language theorem (“The hardest context-free language”, SIAM J. Comp., 1973, http://dx.doi.org/10.1137/0202025 ) for the classical family of LL([Formula: see text]) languages. The first result is that there is a language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form, to which every language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form can be reduced by a homomorphism, that is, [Formula: see text] if and only if [Formula: see text]. Then it is shown that this statement does not hold for the full class of LL([Formula: see text]) languages. The other hardest language theorem is then established in the following form: there is a language [Formula: see text] defined by an LL(1) grammar in the Greibach normal form, such that, for every language [Formula: see text] defined by an LL([Formula: see text]) grammar, with [Formula: see text], there exists a homomorphism [Formula: see text], for which [Formula: see text] if and only if [Formula: see text] [Formula: see text] [Formula: see text], where [Formula: see text] is a new symbol. The results lead to two robust language families: the closures of the languages defined by LL(1) grammars in the Greibach normal form under inverse homomorphisms and under inverse finite transductions.
Publisher
World Scientific Pub Co Pte Ltd
Subject
Computer Science (miscellaneous)
Cited by
1 articles.
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