Skip to main content
SpringerLink
Log in

The theory of languages

  • Published:
Mathematical systems theory Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

References

  1. A. V. Aho, “Indexed grammars, an extension of context free grammars”, Princeton Univ. Doct. Thesis, 1967. Also seeIEEE Conf. Record of Eighth Annual Symp. on Switching and Automata Theory. Austin, Tex., October, 1967.

  2. A. V. Aho, J. E. Hopcroft andJ. D. Ullman, Tape and time complexity of pushdown automaton languages,Information and Control, to appear.

  3. Y. Bar-Hillel, M. Perles andE. Shamir, On formal properties of simple phrase structure grammars,Z. Phonetik Sprachwiss. Kommunikat. 14 (1961), 143–172.

    Google Scholar 

  4. D. C. Cantor, On the ambiguity problem of Backus systems,J. Assoc. Comput. Mach. 9 (1962), 477–479.

    Google Scholar 

  5. N. Chomsky, “Context-free grammars and pushdown storage”,Quart. Prog. Dept. No.65 M.I.T. Res. Lab. Elect., 1962, pp. 187–194.

    Google Scholar 

  6. N. Chomsky, “Formal properties of grammars”, pp. 323–418,Handbook of Math. Psych., Vol. 2, Wiley, New York, 1963.

    Google Scholar 

  7. N. Chomsky, “Introduction to the formal analysis of natural languages”, pp. 269–321,Handbook of Math. Psych., Vol. 2, Wiley, New York, 1963.

    Google Scholar 

  8. N. Chomsky, On certain formal properties of grammars,Information and Control 2 (1959), 137–167.

    Google Scholar 

  9. N. Chomsky, “Three models for the description of language”,PGIT, 2:3, September, 1956, pp. 113–124.

    Google Scholar 

  10. N. Chomsky andM. P. Schützenberger, “The algebraic theory of context free languages”, pp. 118–161,Computer Programming and Formal Systems North Holland, Amsterdam, 1963.

    Google Scholar 

  11. J. Evey, “The theory and application of pushdown store machines”, Harvard Univ. Doct. Thesis, 1963.

  12. P. C. Fischer, “Multi-tape and infinite state automata—a survey”,CACM, 8:12, December, 1965, pp. 799–805.

    Google Scholar 

  13. R. W. Floyd,New Proofs and Old Theorems in Logic and Formal Linguistics Computer Associates Inc., Wakefield, Mass., 1964.

    Google Scholar 

  14. R. W. Floyd, On ambiguity in phrase structure languages,Comm. ACM 5 (1962), 526–534.

    Google Scholar 

  15. R. W. Floyd, “The syntax of programming languages—a survey”,PGEC, 13:4, August, 1964, pp. 346–353.

    Google Scholar 

  16. S. Ginsburg, Examples of abstract machines,IRE Trans. EC-11 (1962), 132–135.

    Google Scholar 

  17. S. Ginsburg,The Mathematical Theory of Context-Free Languages McGraw-Hill, New York, 1966.

    Google Scholar 

  18. S. Ginsburg andS. A. Greibach, “Abstract families of languages”,IEEE Conf. Record of Eighth Annual Symp. on Switching and Automata Theory, Austin, Tex., October, 1967.

  19. S. Ginsburg andS. A. Greibach, Deterministic context free languages,Information and Control 9 (1966), 620–648.

    Google Scholar 

  20. S. Ginsburg andS. A. Greibach, Mappings which preserve context sensitive languages,Information and Control 9 (1966), 563–582.

    Google Scholar 

  21. S. Ginsburg, S. A. Greibach andM. A. Harrison, One-way stack automata,J. Assoc. Comput. Mach. 14 (1967), 389–418.

    Google Scholar 

  22. S. Ginsburg, S. A. Greibach andM. A. Harrison, Stack automata and compiling,J. Assoc. Comput. Mach. 14 (1967), 172–201.

    Google Scholar 

  23. S. Ginsburg andJ. E. Hopcroft, “Two-way balloon automata and AFL's”, System Develop. Corp., Santa Monica, Calif., to appear.

  24. S. Ginsburg andH. G. Rice, Two families of languages related toAlgol,J. Assoc. Comput. Mach. 9 (1962), 350–371.

    Google Scholar 

  25. S. Ginsburg andG. F. Rose, Operations which preserve definability in languages,J. Assoc. Comput. Mach. 10 (1963), 175–195.

    Google Scholar 

  26. S. Ginsburg andG. F. Rose, Some recursively unsolvable problems inAlgol-like languages,J. Assoc. Comput. Mach. 10 (1963), 29–47.

    Google Scholar 

  27. S. Ginsburg andE. H. Spanier, BoundedAlgol-like languages,Trans. Amer. Math. Soc. 113 (1964), 333–368.

    Google Scholar 

  28. S. Ginsburg andE. H. Spanier, Finite turn pushdown automata,J. SIAM Control 4 (1966), 429–453.

    Google Scholar 

  29. S. Ginsburg andE. H. Spanier, Quotients of context-free languages,J. Assoc. Comput. Mach. 10 (1963), 487–492.

    Google Scholar 

  30. S. Ginsburg andJ. Ullian, Ambiguity in context-free languages,J. Assoc. Comput. Mach. 13 (1966), 62–88.

    Google Scholar 

  31. S. Ginsburg andJ. Ullian, Preservation of unambiguity and inherent ambiguity in context-free languages,J. Assoc. Comput. Mach. 13 (1966), 364–368.

    Google Scholar 

  32. J. N. Gray, M. A. Harrison andO. Ibarra, Two-way pushdown automata,Information and Control 11 (1967), 30–70.

    Google Scholar 

  33. S. A. Greibach, A new normal form theorem for context-free phrase structure grammars,J. Assoc. Comput. Mach. 12 (1965), 42–52.

    Google Scholar 

  34. S. A. Greibach, The undecidability of the ambiguity problem for minimal linear grammars,Information and Control 6 (1963), 117–125.

    Google Scholar 

  35. S. A. Greibach, The unsolvability of the recognition of linear context-free languages,J. Assoc. Comput. Mach. 13 (1966), 582–587.

    Google Scholar 

  36. S. A. Greibach andJ. E. Hopcroft, “Independence of AFL operations”, Systems Develop. Corp., Santa Monica, Calif., to appear.

  37. M. Gross, Inherent ambiguity of minimal linear grammars,Information and Control 7 (1964), 366–368.

    Google Scholar 

  38. L. H. Haines, Note on the complement of a (minimal) linear language,Information and Control 7 (1964), 307–314.

    Google Scholar 

  39. J. Hartmanis, P. M. Lewis II andR. E. Stearns, “Hierarchies of memory limited computations”, pp. 179–190,IEEE Conf. Record on Switching Circuit Theory and Logical Design, Ann Arbor, Mich., October, 1965.

  40. J. Hartmanis andR. E. Stearns, On the computational complexity of algorithms,Trans. Amer. Math. Soc. 117 (1965), 285–306.

    Google Scholar 

  41. F. C. Hennie andR. E. Stearns, Two tape simulation of multitape Turing machines,J. Assoc. Comput. Mach. 13 (1966), 533–546.

    Google Scholar 

  42. T. Hibbard andJ. Ullian, The independence of inherent ambiguity from complementedness among context-free languages,J. Assoc. Comput. Mach. 13 (1966), 588–593.

    Google Scholar 

  43. J. E. Hopcroft andJ. D. Ullman, “A survey of formal language theory”, pp. 68–75,Proc. First Annual Princeton Conf. on Inf. Sciences and Systems, Princeton, N. J., March, 1967.

  44. J. E. Hopcroft andJ. D. Ullman, An approach to a unified theory of automata,Bell System Tech. J. 46 (1967), 1793–1827. Also,IEEE Conf. Record of Eighth Annual Symp. on Switching and Automata Theory, Austin, Tex., October, 1967.

    Google Scholar 

  45. J. E. Hopcroft andJ. D. Ullman, Decidable and undecidable questions about automata,J. Assoc. Comput. Mach. 15 (1968).

  46. J. E. Hopcroft andJ. D. Ullman, “Deterministic stack automata and the quotient operator”,JCSS, 1:4, Feb. 1968. Also, “Two results on one-way stack automata”,IEEE Conf. Record of Eighth Annual Symp. on Switching and Automata Theory, Austin, Tex., October, 1967.

  47. J. E. Hopcroft andJ. D. Ullman, “Nonerasing stack automata”,JCSS 1:2, August, 1967, pp. 166–186.

    Google Scholar 

  48. J. E. Hopcroft andJ. D. Ullman, Sets accepted by one-way stack automata are context-sensitive, submitted toInformation and Control. Also, “Two results on one-way stack automata”,IEEE Conf. Record of Eighth Annual Symp. on Switching and Automata Theory, Austin, Tex., October, 1967.

  49. J. E. Hopcroft andJ. D. Ullman, Some results on tape bounded Turing machines, submitted toJ. Assoc. Comput. Mach.

  50. J. E. Hopcroft andJ. D. Ullman, Relations between time and tape complexity,J. Assoc. Comput. Mach., to appear.

  51. S. C. Kleene, “Representation of events in nerve nets and finite automata”, pp. 3–42,Automata Studies Princeton Univ. Press, Princeton, N. J., 1956.

    Google Scholar 

  52. D. E. Knuth, On the translation of languages from left to right,Information and Control 8 (1965), 607–639.

    Google Scholar 

  53. A. J. Korenjak andJ. E. Hopcroft, “Simple deterministic languages”, pp. 36–46,IEEE Conf. Record of Seventh Annual Symp. on Switching and Automata Theory, Berkeley, Calif., October, 1966.

  54. S. Y. Kuroda, Classes of languages and linear-bounded automata,Information and Control 7 (1964), 207–223.

    Google Scholar 

  55. P. S. Landweber, Decision problems of phrase structure grammars,IRE Trans. EC-13 (1964), 354–362.

    Google Scholar 

  56. P. S. Landweber, Three theorems on phrase structure grammars of type 1,Information and Control 6 (1963), 131–136.

    Google Scholar 

  57. P. M. Lewis, R. E. Stearns andJ. Hartmanis, “Memory bounds for recognition of context free and context sensitive languages”, pp. 191–202,IEEE Conf. Record on Switching Circuit Theory and Logical Design, Ann Arbor, Mich., October, 1965.

  58. R. McNaughton, Parenthesis grammars,J. Assoc. Comput. Mach. 14 (1967), 490–500.

    Google Scholar 

  59. M. L. Minsky,Computation: Finite and Infinite Machines Prentice-Hall, Inc., Englewood Cliffs, N. J., 1967.

    Google Scholar 

  60. M. L. Minsky, Recursive unsolvability of Post's problem of “tag” and other topics in the theory of Turing machines,Ann. of Math. (2)74 (1961), 437–455.

    Google Scholar 

  61. E. F. Moore, “Gedanken experiments on sequential machines”, pp. 129–153,Automata Studies Princeton Univ. Press. Princeton, N. J., 1956.

    Google Scholar 

  62. J. Myhill, “Linear bounded automata”,WADD Tech. Note, no. 60-165, Wright Patterson Air Force Base, Ohio, 1960.

    Google Scholar 

  63. R. J. Parikh, “Language generating devices”,Quart. Prog. Rept. no. 60, M.I.T. Res. Lab. Elect., 1961, pp. 199–212. This paper has been reprinted as “On context-free languages”,J. Assoc. Comput. Mach. 13 (1966), 570–581.

    Google Scholar 

  64. E. Post, A variant of a recursively unsolvable problem,Bull. Amer. Math. Soc. 52 (1946), 264–268.

    Google Scholar 

  65. M. O. Rabin, Real-time computation,Israel J. Math. 1 (1963), 203–211.

    Google Scholar 

  66. M. O. Rabin andD. Scott, “Finite automata and their decision problems”,IBM. J. Res. Develop. 3 (1959), 115–125. Also inSequential Machines: Selected Papers, pp. 63–91, (E. F. Moore, ed.), Addison-Wesley, Reading, Mass., 1964.

    Google Scholar 

  67. D. J. Rosenkrantz, Matrix equations and normal forms for context-free grammars,J. Assoc. Comput. Mach. 14 (1967), 501–507.

    Google Scholar 

  68. D. J. Rosenkrantz, “Programmed grammars—a new device for generating formal languages”, Columbia Univ. Doct. Thesis, 1967. Also seeIEEE Conf. Record of Eighth Annual Symp. on Switching and Automata Theory, Austin, Tex., October, 1967.

  69. S. Scheinberg, Note on the Boolean properties of context free languages,Information and Control 3 (1960), 372–375.

    Google Scholar 

  70. M. P. Schützenburger, Finite counting automata,Information and Control 5 (1962), 91–107.

    Google Scholar 

  71. E. Shamir, On sequential languages,Z. Phonetik Sprachwiss. Kommunikat. 18 (1965), 61–69.

    Google Scholar 

  72. R. J. Stanley, “Finite state representations of context free languages”,Quart. Prog. Rept. no. 76, M.I.T. Res. Lab. Elect., 1965, pp. 276–279.

  73. R. E. Stearns, A regularity test for pushdown machines,Information and Control, to appear.

  74. A. M. Turing, On computable numbers with an application to the Entscheidungsproblem,Proc. London Math. Soc. (2)42 (1936), 230–265; Correction,ibid., (2)43 (1937), 544–546.

    Google Scholar 

  75. H. Yamada, Real-time computation and recursive functions not real-time computable,IRE Trans. EC-11 (1962), 753–760.

    Google Scholar 

  76. D. H. Younger, Recognition and parsing of context-free languages in timen 3,Information and Control 10 (1967), 189–208.

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Bell Telephone Laboratories, Inc., Murray Hill, New Jersey, USA

    Alfred V. Aho & Jeffrey D. Ullman

Authors
  1. Alfred V. Aho
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jeffrey D. Ullman
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Aho, A.V., Ullman, J.D. The theory of languages. Math. Systems Theory 2, 97–125 (1968). https://doi.org/10.1007/BF01692510

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01692510

Keywords

Search

Navigation