Summary
A new method for transforming grammars into equivalent LL(k) grammars is studied. The applicability of the transformation is characterized by defining a subclass of LR(k) grammars, called predictive LR(k) grammars, with the property that a grammar is predictive LR(k) if and only if the corresponding transformed grammar is LL(k). Furthermore, it is shown that deterministic bottom-up parsing of a predictive LR(k) grammar can be done by the LL(k) parser of the transformed grammar. This parsing method is possible since the transformed grammar always ‘left-to-right covers’ the original grammar. The class of predictive LR(k) grammars strictly includes the class of LC(k) grammars (the grammars that can be parsed deterministically in the left-corner manner). Thus our transformation is more powerful than the one previously available, which transforms LC(k) grammars into LL(k) form.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Aho, A.V., Ullman, J.D.: The Theory of Parsing, Translation, and Compiling, Vol. I: Parsing. Englewood Cliffs, N.J.: Prentice-Hall 1972
Aho, A.V., Ullman, J.D.: The Theory of Parsing, Translation, and Compiling, Vol. II: Compiling. Englewood Cliffs, N.J.: Prentice-Hall 1973
Brosgol, B.M.: Deterministic translation grammars. Harvard University, Cambridge, Mass., Ph.D. Thesis, 1974
Burge, W.H.: Recursive Programming Techniques. Reading, Mass.: Addison-Wesley 1975
Cheatham, T.E., Jr.: The Theory and Construction of Compilers. Wakefield, Mass.: Computer Associates 1967
Demers, A.: Generalized left corner parsing. Conf. Record of the Fourth ACM Symposium on Principles of Programming Languages, pp. 170–182 (1977)
Foster, J.M.: A syntax improving program. Comput. J. 11, 31–34 (1968)
Greibach, S.A.: A new normal-form theorem for context-free phrase structure grammars. J. Assoc. Comput. Mach. 12:1, 42–52 (1965)
Griffiths, M.: LL(1) grammars and analysers. In: Compiler Construction: An Advanced Course, Lecture Notes in Computer Science, Vol. 21 (F.L. Bauer, J. Eickel, eds.), pp. 57–84. Berlin-Heidelberg-New York: Springer 1974
Griffiths, T.V., Petrick, S.R.: On the relative efficiencies of context-free grammar recognizers. Comm. ACM. 8, 289–300 (1965)
Griffiths, T.V., Petrick, S.R.: Top-down versus bottom-up analysis. In: Proc. of the IFIP congress 68, Vol. 1 (A.J.H. Morrell, ed.), pp. 80–85. Amsterdam: North-Holland 1969
Hammer, M.: A new grammatical transformation into deterministic top-down form. MIT, Mass., Project MAC Technical Report TR-119, 1974
Hammer, M.: A new grammatical transformation into LL(k) form. Proc. of Sixth Annual ACM Symposium on Theory of Computing, pp. 266–275 (1974)
Hopgood, F.R.A.: Compiling Techniques. New York, N.Y.: American Elsevier 1969
Irons, E.T.: A syntax directed compiler for ALGOL 60. Comm. ACM. 4, 51–55 (1961)
Knuth, D.E.: On the translation of languages from left to right. Information and Control 8, 607–639 (1965)
Knuth, D.E.: Top-down syntax analysis. Acta Informat. 1, 79–110 (1971)
Komor, T.: A note on left factored languages. Comput. J. 17, 242–244 (1974)
Kurki-Suonio, R.: On top-to-bottom recognition and left recursion. Comm. ACM. 9, 527–528 (1966)
Kurki-Suonio, R.: Notes on top-down languages. BIT 9, 225–238 (1969)
Lewis, P.M., II, Rosenkrantz, D.J., Stearns, R.E.: Compiler Design Theory. Reading, Mass.: Addison-Wesley 1976
Lewis, P.M., II, Stearns, R.E.: Syntax directed transduction. J. Assoc. Comput. Mach. 15, 464–488 (1968)
Nijholt, A.: On the covering of left-recursive grammars. Conf. Record of the Fourth ACM Symposium on Principles of Programming Languages, pp. 86–96 (1977)
Rosenkrantz, D.J.: Matrix equations and normal forms for context-free grammars. J. Assoc. Comput. Mach. 14, 501–507 (1967)
Rosenkrantz, D.J., Lewis, P.M., II: Deterministic left corner parsing. IEEE Conf. Record of 11th Annual Symposium on Switching and Automata Theory, pp. 139–152 (1970)
Rosenkrantz, D.J., Stearns, R.E.: Properties of deterministic top-down grammars. Information and Control 17, 226–256 (1970)
Soisalon-Soininen, E.: Characterization of LL(k) languages by restricted LR(k) grammars. Department of Computer Science, University of Helsinki, Helsinki, Report A-1977-3, 1977
Soisalon-Soininen, E., Ukkonen, E.: A characterization of LL(k) languages. In: Automata, Languages and Programming, Third Colloquium (S. Michaelson, R. Milner, eds.), pp. 20–30. Edinburgh: Edinburgh University Press 1976
Stearns, R.E.: Deterministic top-down parsing. Proc. Fifth Annual Princeton Conf. on Information Sciences and Systems, pp. 182–188 (1971)
Wood, D.: The normal form theorem — another proof. Comput. J. 12, 139–147 (1969)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Soisalon-Soininen, E., Ukkonen, E. A method for transforming grammars into LL(k) form. Acta Informatica 12, 339–369 (1979). https://doi.org/10.1007/BF00268320
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF00268320