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Normal Form Algorithms for Extended ContextFree Grammars
 Theoretical Computer Science
, 2000
"... We investigate the complexity of a variety of normalform transformations for extended contextfree grammars, where by extended we mean that the set of righthand sides for each nonterminal in such a grammar is a regular set. The study is motivated by the implementation project GraMa which will p ..."
Abstract

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We investigate the complexity of a variety of normalform transformations for extended contextfree grammars, where by extended we mean that the set of righthand sides for each nonterminal in such a grammar is a regular set. The study is motivated by the implementation project GraMa which will provide a C++ toolkit for the symbolic manipulation of contextfree objects just as Grail does for regular objects. Our results generalize known complexity bounds for contextfree grammars but do so in nontrivial ways. Specifically, we introduce a new representation scheme for extended contextfree grammars (the symbolthreaded expression forest), a new normal form for these grammars (dot normal form) and new regular expression algorithms. 1 Introduction In the 1960's, extended contextfree grammars were introduced, based on BackusNaur form, as a useful abbreviatory notation that made contextfree grammars easier to write. More recently, the Standardized General Markup Language (SGML...