Abstract
This paper presents a formal account of the grammar system described informally in the previous issue of CaT. LA-grammar is proven to generate all and only the recursive languages. The classes of regular, context-free, and context-sensitive languages are reconstructed in LA-grammar. The relation between LA-grammar and associated parsers and generators is shown to be ‘type transparent’, and illustrated with examples. Finally, differences between LA-grammar and Finite State Automata, RTNs, ATNs, and Predictive Analyzers are explained.
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References
Aho, A. V., and J. D. Ullman. 1972.The Theory of Parsing, Translation, and Compiling. Vol.I: Parsing. Englewood Cliffs, New Jersey: Prentice Hall.
Aho, A. V., and J. D. Ullman. 1979.Principles of Compiler Design. Reading, Massachusetts: Addison-Wesley.
Alt, F.L. and I. Rhodes. 1961. Recognition of Clauses and Phrases in Machine Translation of Languages. Proceedings of the First International Conference on Machine Translation of Languages and Applied Language Analaysis.
Bar-Hillel, Y. 1953. A Quasi-arithmetical Notation for Syntactic Description.Language 29.
Barton, G. E., R. C. Berwick, and E. S. Ristad. 1987.Computational Complexity and Natural Language. Cambridge, Massachusetts: MIT Press.
Berwick, R. C., and A. S. Weinberg. 1984.The Grammatical Basis of Linguistic Performance: Language Use and Aquisition. Cambridge, Massachusetts: MIT Press.
Earley, J. 1970. An Efficient Context-Free Parsing Algorithm.CACM 13(2):94–102.
Hausser, R. 1985. Left-associative Grammar and the Parser NEWCAT. Technical Report IN-CSLI-85-5. Center for the Study of Language and Information, Stanford University.
Hausser, R. 1986.NEWCAT: Parsing Natural Language Using Left-associative Grammar. Lecture Notes in Computer Science. Berlin: Springer-Verlag.
Hausser, R. 1987. Left-Associative Grammar: Theory and Implementation. Technical Report CMU-CMT-87-104. Center for Machine Translation, Carnegie Mellon University, Pittsburgh, PA.
Hausser, R. 1988a. Left-Associative Grammar, an Informal Outline.Computers and Translation. 3:23–67. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Hausser, R. 1988b. The Computational Complexity of Left-Associative Grammar, Proceedings of the Second International Conference on Theoretical and Methodological Issues in Machine Translation, Carnegie Mellon University, Pittsburgh, PA. June 12–14, 1988.
Hausser, R. (forthcoming).Computation of Language. Berlin: Springer-Verlag. 1988.
Hopcroft, J. E., and Ullman, J. D. 1979.Introduction to Automata Theory, Languages, and Computation. Reading, Massachusetts: Addison-Wesley.
Kuno, S. and A. Oettinger. 1963. Multiple Path Syntactic Analyzer. In: C. M. Popplewell (ed).Information Processing-62, p. 306–312. Amsterdam: North-Holland.
Oettinger, A. G. 1961. Automatic Syntactic Analysis and the Pushdown Store. Proceedings of Symposia in Applied Mathematics. American Mathematical Society, 12.
Rhodes, I. 1959. A New Approach to the Mechanical Translation of Russian. NBS Report No. 6295.
Sherry, M. 1961. Comprehensive Report on Predictive Syntactic Analysis. Mathematical Linguistics and Automatic Translation, Report No. NSF-7, Section I, Harvard Computation Laboratory.
Tomita, M. 1986.Efficient Parsing for Natural Languages. Dordrecht, The Netherlands: Kluwer Academic Publishers.
Woods, W. A. 1970. Transition Network Grammars for Natural Language Analysis.CACM 3(10):591–606.
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Hausser, R. Left-associative grammar: The algebraic definitions. Mach Translat 3, 121–155 (1988). https://doi.org/10.1007/BF02055235
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DOI: https://doi.org/10.1007/BF02055235