Abstract
This chapter is devoted to context-free languages. Context-free languages and grammars were designed initially to formalize grammatical properties of natural languages [9]. They subsequently appeared to be well adapted to the formal description of the syntax of programming languages. This led to a considerable development of the theory.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
A. V. Aho and J. D. Ullman. The Theory of Parsing, Translation and Compiling., volume 1. Prentice-Hall, 1973.
J.-M. Autebert. Théorie des langages et des automates. Masson, 1994.
J.-M. Autebert, L. Boasson, and I. H. Sudborough. Some observations on hardest context-free languages. Technical Report 81–25, Rapport LITP, April 1981.
J. Berstel. Transductions and Context-Free Languages. Teubner Verlag, 1979.
M. Blattner and S. Ginsburg. Canonical forms of context-free grammars and position restricted grammar forms. In Karpinski, editor, Fundamentals of Computing Theory, volume 56 of Lect. Notes Comp. Sei., 1977.
L. Boasson. Two iteration theorems for some families of languages. J. Comput. System Sei., 7(6):583–596, December 1973.
L. Boasson, J. P. Crestin, and M. Nivat. Familles de langages translatables et fermées par crochet. Acta Inform., 2:383–393, 1973.
F. J. Brandenburg. On the intersection of stacks and queues. Theoret. Comput. Sci., 23:69–82, 1983.
N. Chomsky. On certain formal properties of grammars. Inform. and Control, 2:137–167, 1959.
N. Chomsky and M. P. Schützenberger. The algebraic theory of context-free languages. In P. Bradford and D. Hirschberg, editors, Computer programming and formal systems, pages 118–161. North-Holland (Amsterdam), 1963.
S. V. Cole. Deterministic pushdown store machines and realtime computation. J. Assoc. Comput. Mach., 18:306–328, 1971.
B. Courcelle. On jump deterministic pushdown automata. Math. Systems Theory, 11:87–109, 1977.
A. Cremers and S. Ginsburg. Context-free grammar forms. J. Comput. System Sci., 11:86–117, 1975.
R. J. Evey. The theory and application of pushdown store machines. In Mathematical Linguistics and Automatic Translation, NSF-IO, pages 217–255. Harvard University, May 1963.
M. Fliess. Transductions de séries formelles. Discrete Math., 10:57–74, 1974.
R. W. Floyd. Syntactic analysis and operator precedence. J. Assoc. Comput. Mach., 10:313–333, 1963.
S. Ginsburg. The Mathematical Theory of Context-Free Languages. McGraw-Hill, 1966.
S. Ginsburg, J. Goldstine, and S. Greibach. Some uniformely erasable families of languages. Theoret. Comput. Sci., 2:29–44, 1976.
S. Ginsburg and M. A. Harrison. Bracketed context-free languages. J. Comput. System Sei., 1:1–23, 1967.
S. Ginsburg and H. G. Rice. Two families of languages related to ALGOL. J. Assoc. Comput. Mach., 9:350–371, 1962.
S. Ginsburg and E. Spanier. Finite-turn pushdown automata. SIAM J. Control, 4:429–453, 1966.
S. Ginsburg and E. Spanier. Derivation-bounded languages. J. Comput. System Sei., 2:228–250, 1968.
S. Greibach. The hardest context-free language. SIAM J. Comput., 2:304–310, 1973.
S. A. Greibach. A new normal form theorem for context-free phrase structure grammars. J. Assoc. Comput. Mach., 12(1):42–52, 1965.
S. A. Greibach. Jump pda’s, deterministic context-free languages, principal afdl’s and polynomial time recognition. In Proc. 5th Annual ACM Conf. Theory of Computing, pages 20–28, 1973.
S. A. Greibach. Jump pda’s and hierarchies of deterministic cf languages. SIAM J. Comput., 3:111–127, 1974.
J. Gruska. A few remarks on the index of context-free grammars and languages. Inform. and Control, 19:216–223, 1971.
M. A. Harrison. Introduction to Formal Language Theory. Addison-Wesley, 1978.
J. E. Hoperoft and J. D. Ullman. Formal Languages and Their Relation to Automata. Addison-Wesley, 1969.
J. E. Hoperoft and J. D. Ullman. Introduction to Automata Theory, Languages and Computation. Addison-Wesley, 1979.
G. Hotz. Normal form transformations of context-free grammars. Acta Cybernetics, 4(1):65–84, 1978.
G. Hotz and K. Estenfeld. Formale Sprachen. B.I.-Wissenschaftsverlag, 1981.
G. Hotz and T. Kretschmer. The power of the Greibach normal form. Elektron. Inforrnationsverarb. Kybernet., 25(10):507–512, 1989.
D.E. Knuth. On the translation of languages from left to right. Inform. and Control, 8:607–639, 1965.
D. E. Knuth. A characterization of parenthesis languages. Inform. and Control, 11:269–289, 1967.
A. J. Korenjack and J. E. Hoperoft. Simple deterministic languages. In Conference record of seventh annual symposium on switching and automata theory, pages 36–46, Berkeley, 1966.
W. Kuich. Formal power series, chapter 9. This volume.
P. M. Lewis and R. E. Stearns. Syntax-directed transduction. J. Assoc. Comput. Mach., 15(3):465–488, 1968.
R. McNaughton. Parenthesis grammars. J. Assoc. Comput. Mach., 14(3):490–500, 1967.
M. Nivat. Transductions des langages de Chomsky, Ch. VI,miméographié. PhD thesis, Université de Paris, 1967.
M. Nivat. Transductions des langages de Chomsky. Annales de l’Institut Fourier, 18:339–456, 1968.
M. Oyamaguchi. The equivalence problem for realtime dpda’s. J. Assoc. Corn-put. Mach., 34:731–760, 1987.
R. J. Parikh. On context-free languages. J. Assoc. Comput. Mach., 13:570–581, 1966.
D. L. Pilling. Commutative regular equations and Parikh’s theorem. J. London Math. Soc., 6:663–666, 1973.
D. J. Rosenkrantz. Matrix equations and normal forms for context-free grammars. J. Assoc. Comput. Mach., 14:501–507, 1967.
Jacques Sakarovitch. Pushdown automata with terminal languages. In Languages and Automata Symposium, number 421 in Publication RIMS, Kyoto University, pages 15–29, 1981.
A. Salomaa. Formal Languages. Academic Press, 1973.
M. P. Schützenberger. On context-free languages and pushdown automata. Inform. and Control, 6:217–255, 1963.
G. Sénizergues. The equivalence and inclusion problems for NTS languages. J. Comput. System Sci., 31:303–331, 1985.
G. Sénizergues. Church-Rosser controlled rewriting systems and equivalence problems for deterministic context-free languages. Inform. Comput., 81:265–279, 1989.
E. Shamir. A representation theorem for algebraic and context-free power series in noncommuting variables. Inform. Comput., 11:39–254, 1967.
S. Sippu and E. Soisalon-Soininen. Parsing Theory, Vol I. EATCS Monographs on Theoretical Computer Science. Springer-Verlag, 1988.
L. Valiant. The equivalence problem for deterministic finite turn pushdown automata. Inform. and Control, 25:123–133, 1974.
H. Wechler. Characterization of rational and algebraic power series. RA IRO Inform. Théor., 17:3–11, 1983.
M. K. Yntema. Inclusion relations among families of context-free languages. Inform. and Control, 10:572–597, 1967.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Autebert, JM., Berstel, J., Boasson, L. (1997). Context-Free Languages and Pushdown Automata. In: Rozenberg, G., Salomaa, A. (eds) Handbook of Formal Languages. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-59136-5_3
Download citation
DOI: https://doi.org/10.1007/978-3-642-59136-5_3
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-63863-3
Online ISBN: 978-3-642-59136-5
eBook Packages: Springer Book Archive