Abstract
A technique that represents derivations of a context-free grammarG over a semiring and that obtains for a wordw inL(G) the set of all canonical parses forw has previously been described. A state grammar is one of a collection of grammars that place restrictions on the manner of application of context-free-like productions and that generate a noncontext-free language. The “context-free” properties of a state grammar have been used to extend the algebraic parsing technique for languages generated by state grammars,viz., context-sensitive languages. The extension for state grammars is not unlike that required for other types of grammars in whose collection state grammars are representative.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
S. Abraham, “Some questions of phrase structure grammars I,”Comput. Linguist. 4:61–70 (1965).
S. Greibach and J. Hopcroft, “Scattered context grammars,”J. Comput. Syst. Sci. 3: 233–247 (1969).
O. Ibarra, “Simple matrix languages,”Inf. Control 17:359–394 (1970).
T. Kasai, “An hierarchy between context-free and context-sensitive languages,”J. Comput Syst. Sci. 4:492–508 (1970).
D. Rosencrantz, “Programmed grammars and classes of formal languages,”J. Assoc. Comput. Mach. 16: 107–131 (1969).
A. Salomaa, “Periodically time-variant context-free grammars,”Inf. Control 17:294–311 (1970).
A. Salomaa, “Matrix grammars with a leftmost restriction,”Inf. Control 20:143–149 (1972).
O. Mayer, “Some restrictive devices for context-free grammars,”Inf. Control 20:69–92 (1972).
A. B. Cremers, “Normal forms for context-sensitive grammars,”Acta Inf. 3:59–73 (1973).
S. Weiss, G. Magó, and D. Stanat, “An Algebraic Parsing Theorem for Context-Free Languages,” inAutomata, Languages and Programming, M. Nivat, ed. (North Holland, Amsterdam, 1973).
R. Cannon, “State Grammar Parsing,” Ph.D. Dissertation, University of North Carolina, Chapel Hill, N.C. (1973).
R. Cannon, “Phrase structure grammars generating context-free languages,”Inf. Control 29: 252–267 (1975).
N. Chomsky and M. Schützenberger, “The Algebraic Theory of Context-Free Languages,” inComputer Programming and Formal Systems, P. Braffort and D. Hirschberg, eds. (North Holland, Amsterdam, 1963).
R. Evey, “The Theory and Application of Pushdown Store Machines,” Ph.D. Dissertation, Harvard University (1963).
G. Matthews, “Discontinuity and asymmetry in phrase structure grammars,”Inf. Control 6:137–146 (1963).
J. Thatcher, “Characterizing derivation trees of context-free grammars through a generalization of finite automata theory,”J. Comput. Syst. Sci. 1:317–322 (1967).
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Cannon, R.L. An algebraic technique for context-sensitive parsing. International Journal of Computer and Information Sciences 5, 257–276 (1976). https://doi.org/10.1007/BF00991838
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF00991838