Joseph Bates
Abstract
LR parsing techniques have long been studied as being efficient and powerful methods for processing context-free languages. A linear-time algorithm for recognizing languages representable by LR(k) grammars has long been known. Recognizing substrings of a context-free language is at least as hard as recognizing full strings of the language, since the latter problem easily reduces to the former. In this article we present a linear-time algorithm for recognizing substrings of LR(k) languages, thus showing that the substring recognition problem for these languages is no harder than the full string recognition problem. An interesting data structure, the Forest-Structured Stack, allows the algorithm to track all possible parses of a substring without loosing the efficiency of the original LR parser. We present the algorithm, prove its correctness, analyze its complexity, and mention several applications that have been constructed.
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Index Terms
- Recognizing substrings of LR(k) languages in linear time
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Reviews
Marian Gheorghe
The problem of recognizing the substrings of LR(k) languages is addressed. A detailed description of the algorithm in the case of one lookahead symbol is given in the second section. An interesting data structure, called a forest-structured stack, is used by the algorithm. Other algorithms parse the substrings of a language [1] by modifying the LR parsing tables of the classical approach [2]; in contrast, the algorithm presented in this paper modifies the parsing algorithm itself and does not require any changes in the original LR tables. It is important that this method has a linear time complexity, the same as that of the original LR parsing algorithm. The algorithm is slightly modified, in the fifth section, to deal with canonical LR(k) grammars, for k?2 . The correctness and the complexity of the algorithm are established in the third and fourth sections<__?__Pub Caret>. The conclusions mention that a first version of the algorithm was developed by the first author in 1980 and was applied as a basis for syntax checking in the XEDIT editor. New results concerning the application of this recognition algorithm in different editor systems as a syntax checker and in the areas of speech recognition and parsing natural languages are also reported. Because of its linear time complexity, this algorithm seems to be appropriate for different applications involving substring recognition.
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