Abstract
A grammar formF defines via a so-calledinterpretation mechanism, a family of languages
(F). In this paper we establish that for many grammar formsF,
(the family of context-free languages) implies
(F)=
RE (the family of recursively enumerable sets). We conjecture that this is also true in general. Because of this, it seems necessary to use restricted interpretations for non context-free grammar forms, a form giving then rise to a family
We compare the obvious alternatives for restricting interpretations and focus attention on two promising alternatives,
Q (F) and
st(F) and their combination
Q, st(F). Using st-interpretations, surprising families can be generated and strong normal form results can be obtained. Closure results and decidability results are also given. UnderQ, st-interpretation, it is possible to characterize a number of well-known families of languages between
CF and
RE, including the families of EOL, ETOL, matrix and scattered context languages.
Similar content being viewed by others
References
A. B. Cremers, S. Ginsburg, Context-Free Grammar Forms,J. of Computer and System Sciences 11, 86–117, (1975).
A. B. Cremers, O. Mayer, On Vector Languages.J. of Computer and System Sciences 7, 158–166 (1974).
S. Ginsberg,Algebraic and automata-theoretic properties of formal languages. North Holland, Amsterdam, (1975).
S. Ginsburg, E. Spanier, Substitutions of Grammar Forms.Acta Informatica 5, 377–386 (1975).
H. A. Maurer,Theoretische Grundlagen der Programmiersprachen BI, Mannheim, (1969).
H. A. Maurer, A. Salomaa D. Wood, EOL Forms.Acta Informatica 8, 75–96 (1977).
H. A. Maurer, A. Salomaa, D. Wood, Uniform Interpretations ofL Forms.Information and Control 36, 157–173 (1978).
A. Salomaa,Formal Languages. Academic Press, New York (1973).
W. Savitch, How to make arbitrary Grammars look like Context-Free Grammars.SIAM J. Computing 2, 174–182 (1973).
Author information
Authors and Affiliations
Additional information
Part of this work was carried out while the third and fourth authors were visiting the University of Karlsruhe. Part of this work was supported by the Natural Sciences and Engineering Research Council of Canada Grant No. A-7700.
Rights and permissions
About this article
Cite this article
Maurer, H.A., Penttonen, M., Salomaa, A. et al. On non context-free grammar forms. Math. Systems Theory 12, 297–324 (1978). https://doi.org/10.1007/BF01776580
Received:
Revised:
Issue Date:
DOI: https://doi.org/10.1007/BF01776580