Normal form algorithms for extended context-free grammars

Authors:
Jürgen Albert;Dora Giammarresi;Derick Wood
Affiliations:
Univ Würzburg, Am Hubland, Würzburg, Germany;Univ. Ca' Foscari di Venezia, Venice, Mestre, Italy;Hong Kong Univ. of Science & Technology, Hong Kong, People's Republic of China
Venue:
Theoretical Computer Science
Year:
2001

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Abstract

We investigate the complexity of a variety of normal-form transformations for extended context-free grammars, where by extended we mean that the set of right-hand 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 context-free objects just as Grail does for regular objects. Our results generalize known complexity bounds for context-free grammars but do so in nontrivial ways. Specifically, we introduce a new representation scheme for extended context-free grammars (the symbol-threaded expression forest), a new normal form for these grammars (dot normal form) and new regular expression algorithms. Copyright 2001 Elsevier Science B.V.