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Grammars with Controlled Derivations

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Handbook of Formal Languages

Abstract

In [13], N. Chomsky says that “the main problem of immediate relevance to the theory of language is that of determining where in the hierarchy of devices the grammars of natural languages lie.” Formulated in other terms, the question is “where are the natural languages placed in the Chomsky hierarchy?” The debate started in 1959 and is not yet settled. Various arguments over English [4], Mohawk [92], Swiss German [112], Bambara [16], Chinese [95], etc., were given, refuted, rehabilitated — see pro and con arguments as well as further bibliographical information in [38] and [70]. The main difficulty is not a mathematical one but a linguistic one: what is English, what is a natural language, can we separate the syntax and the morphology from semantics or pragmatics? Whatever is or will be the position with respect to these questions, the linguists seem to agree (see again [70]) that “all” natural languages contain constructions which cannot be described by context-free grammars. Three basic such features of natural languages are:

  • reduplication, leading to languages of the form {xx | x ∈ V*}

  • multiple agreements, modeled by languages of the form {a n b n c n | n ≥ 1}, {a n b n c n d n | n ≥ 1}, etc.

  • crossed agreements, as modeled by {a n b m c n d m | n, m ≥ 1}.

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References

  1. S. Abraham, Some questions of phrase-structure grammars, Comput. Linguistics, 4 (1965), 61–70.

    MathSciNet  Google Scholar 

  2. A. V. Aho, Indexed grammars — an extension of context-free grammars, Journal of the ACM, 15 (1968), 647–671.

    MathSciNet  MATH  Google Scholar 

  3. P. R. J. Asveld, Controlled iteration grammars and full hyper-AFLs, Inform. Control. 34 (1976), 248–269.

    MathSciNet  MATH  Google Scholar 

  4. Y. Bar-Hillel, E. Shamir, Finite-state languages: formal representations and adequacy problems, Bull. of Res. Council of Israel, 8 (1960), 155–166.

    MathSciNet  MATH  Google Scholar 

  5. J. Berstel, Transductions and Context-Free Languages, Teubner, Stuttgart, 1979.

    MATH  Google Scholar 

  6. H. Bordihn, Pure languages and the degree of nondeterminism, J. Inform. Process. Cybern., 28 (1992), 231–240.

    MATH  Google Scholar 

  7. H. Bordihn, H. Fernau, Accepting grammars with regulation, Internat. J. Comp. Math., 53 (1994), 1–18.

    MATH  Google Scholar 

  8. H. Bordihn, H. Fernau, Accepting grammars and systems: an overview, Proc. of Development in Language Theory Conf., Magdeburg, 1995, 199–208.

    Google Scholar 

  9. H. Bordihn, H. Fernau, Remarks on accepting parallel systems, Intern. J. Computer Math., 56 (1995), 51–67.

    MATH  Google Scholar 

  10. F. J. Brandenburg, On context-free grammars with regular control set, In: Proc. 7th Conf. Automata and Formal Languages, Salgotarjan, 1993.

    Google Scholar 

  11. F. J. Brandenburg, Erasing in context-free control languages. Petri nets languages make the difference, manuscript, 1994.

    Google Scholar 

  12. H. Bunke, Programmed graph grammars, In: Graph Grammars and their Application to Computer Science and Biology, Lecture Notes in Computer Science 73, Springer-Verlag, Berlin, 1982, 89–112.

    Google Scholar 

  13. N. Chomsky, On certain formal properties of grammars, Inform. Control, 1 (1959), 91–112.

    MathSciNet  MATH  Google Scholar 

  14. A. B. Cremers, O. Mayer, On matrix languages, Inform. Control, 23 (1973), 86–96.

    MathSciNet  MATH  Google Scholar 

  15. K. Culik II, H. A. Maurer, Tree controlled grammars, Computing, 19 (1977), 129–139.

    MathSciNet  MATH  Google Scholar 

  16. C. Culy, The complexity of the vocabulary of Bambara, Linguistic Inquiry, 8 (1985), 345–351.

    Google Scholar 

  17. J. Dassow, Remarks on the complexity of regulated rewriting, Fundamenta Informaticae, 7 (1984), 83–103.

    MathSciNet  MATH  Google Scholar 

  18. J. Dassow, On deterministic random context L systems In: Proc. 2nd Frege Conf., Akademie-Verlag, Berlin, 1984, 309–313.

    Google Scholar 

  19. J. Dassow, On compound Lindenmayer systems, In: The Book of L ( G. Rozenberg, A. Salomaa, eds.), Springer-Verlag, Berlin, 1986, 75–86.

    Google Scholar 

  20. J. Dassow, Pure grammars with regulated rewriting, Rev. Roum. Math. Pures Appl., 31 (1988), 657–666.

    MathSciNet  MATH  Google Scholar 

  21. J. Dassow, On the sequence equivalence problems for OL systems with controlled derivations, Computers and Artificial Intelligence, 7 (1988), 97–105.

    MathSciNet  MATH  Google Scholar 

  22. J. Dassow, Subregularly controlled derivations: context-free case, Rostock Math. Colloq., 34 (1988), 61–70.

    MathSciNet  MATH  Google Scholar 

  23. J. Dassow, U. Fest, On regulated L systems, Rostock Math. Kolloq., 25 (1984), 99–118.

    MathSciNet  MATH  Google Scholar 

  24. J. Dassow, H. Hornig, Conditional grammars with subregular conditions, In: Proc. 2nd Internat. Conf. Words, Languages and Combinatorics, Kyoto, World Scientific, Singapore, 1994, 71–86.

    Google Scholar 

  25. J. Dassow, Gh. Pâun, Further remarks on the complexity of regulated rewriting, Kybernetika, 21 (1985), 213–227.

    MathSciNet  MATH  Google Scholar 

  26. J. Dassow, Gh. Pâun, Further remarks on pure grammars with regulated rewriting, Rev. Roum. Math. Pures Appl., 31 (1986), 855–864.

    MathSciNet  MATH  Google Scholar 

  27. J. Dassow, Gh. Pâun, Regulated Rewriting in Formal Language Theory, Akademie-Verlag, Berlin, and Springer-Verlag, Berlin, 1989.

    MATH  Google Scholar 

  28. H. Ehrig, A. Habel, Graph grammars with application conditions, In: The Book of L ( G. Rozenberg, A. Salomaa, eds.), Springer-Verlag, Berlin, 1986, 87–100.

    Google Scholar 

  29. H. Fernau, On grammar and language families, Fundamenta Informaticae, 25 (1996), 17–34.

    MathSciNet  MATH  Google Scholar 

  30. H. Fernau, A predicate for separating language classes, Bulletin EATCS, 56 (1995), 96–97.

    MATH  Google Scholar 

  31. H. Fernau, Closure properties of ordered languages, Bulletin EATCS, 58 (1996), 159–162.

    MATH  Google Scholar 

  32. H. Fernau, On unconditional transfer, Proc. 21th MFCS Conf., Cracow, Lecture Notes in Computer Science, 1113, Springer-Verlag, Berlin, 1996, 348–359.

    Google Scholar 

  33. R. Freund, Control mechanisms on #-context-free array grammars, In: Mathematical Aspects of Natural and Formal Languages ( Gh. Pâun, ed.), World Scientific, Singapore, 1995, 97–136.

    Google Scholar 

  34. R. W. Floyd, On the non-existence of a phrase-structure grammar for Algol 60, Comm. of the ACM, 5 (1962), 483–484.

    MATH  Google Scholar 

  35. R. Freund, Gh. Pâun, One-dimensional matrix grammars, J. Inform. Process. Cybern., 29 (1993), 357–374.

    MATH  Google Scholar 

  36. I. Fris, Grammars with a partial ordering of the rules, Inform. Control, 12 (1968), 415–425.

    MathSciNet  MATH  Google Scholar 

  37. M. R. Garey, D. J. Johnson, Computers and Intractability. A Guide to the Theory of NP-completeness, Freeman and Co., San Francisco, 1979.

    MATH  Google Scholar 

  38. G. Gazdar, G. K. Pullum, Computationally relevant properties of natural languages and their grammars, New Generation Computing, 3 (1985), 273–306.

    Google Scholar 

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

    MATH  Google Scholar 

  40. S. Ginsburg, Algebraic and Automata-Theoretic Properties of Formal Languages, North-Holland, Amsterdam, 1975.

    MATH  Google Scholar 

  41. S. Ginsburg, G. Rozenberg, TOL schemes and control sets, Inform. Control, 27 (1974), 109–125.

    MathSciNet  MATH  Google Scholar 

  42. S. Ginsburg, E. H. Spanier, Control sets on grammars, Math. Syst. Th., 2 (1968), 159–177.

    MathSciNet  MATH  Google Scholar 

  43. J. Gonczarowski, E Shamir, Pattern selector grammars and several parsing algorithms in the context-free style, J. Comp. Syst. Sci., 30 (1985), 249–273.

    MathSciNet  MATH  Google Scholar 

  44. J. Gonczarowski, M. K. Warmuth, Applications of scheduling theory to formal language theory, Theor. Comp. Sci., 37 (1985), 217–243.

    MathSciNet  MATH  Google Scholar 

  45. J. Gonczarowski, M. K. Warmuth, Scattered and context-sensitive rewriting, Acta Informatica, 20 (1989), 391–411.

    MathSciNet  MATH  Google Scholar 

  46. S. Greibach, J. E. Hoperoft, Scattered context grammars, J. Comp. Syst. Sci., 3 (1969), 233–247.

    MathSciNet  MATH  Google Scholar 

  47. J. Gruska, On a classification of context-free languages, Kybernetika, 13 (1967), 22–29.

    MathSciNet  MATH  Google Scholar 

  48. J. Gruska, The descriptional complexity of context-free languages, In: Proc. 2nd MFCS Conf., 1973, 71–83.

    Google Scholar 

  49. A. Habel, Hyperedge Replacement: Grammars and Languages, Lecture Notes in Computer Science 643, Springer-Verlag, Berlin, 1992.

    MATH  Google Scholar 

  50. A. Habel, R. Heckel, G. Taentzer, Graph grammars with negative application conditions, Fundamente Informaticae,to appear.

    Google Scholar 

  51. M. A. Harrison, Introduction to Formal Language Theory, Addison-Wesley, Reading, 1978.

    MATH  Google Scholar 

  52. T. Harju, A polynomial recognition algorithm for the EDTOL languages, Elektron. Informationsverarb. Kybern., 13 (1977), 169–177.

    MATH  Google Scholar 

  53. D. Hauschildt, M. Jantzen, Petri net algorithms in the theory of matrix grammars, Acta Informatica, 31 (1994), 719–728.

    MathSciNet  MATH  Google Scholar 

  54. F. Hinz, J. Dassow, An undecidability result for regular languages and its application to regulated rewriting, Bulletin EATCS, 38 (1989), 168–173.

    MATH  Google Scholar 

  55. J. E. Hoperoft, J. D. Ullman, Introduction to Automata Theory, Languages, and Computation, Addison-Wesley, Reading, 1979.

    MATH  Google Scholar 

  56. G. Hotz, G. Pitsch, On parsing coupled context-free languages, Theor. Comp. Sci., 161 (1996), 205–233.

    MathSciNet  MATH  Google Scholar 

  57. O. H. Ibarra, Simple matrix languages, Inform. Control, 17 (1970), 359–394.

    MathSciNet  MATH  Google Scholar 

  58. N. D. Jones, S. Skyum, Recognition of deterministic ETOL languages in logarithmic space, Inform. Control, 35 (1977), 177–181.

    MATH  Google Scholar 

  59. N. D. Jones, S. Skyum, Upper bounds on the complexity of some problems concerning L systems, Techn. rep. DA IMI PB-69, University of Aarhus, Dept. of Comp. Sci., 1977.

    Google Scholar 

  60. J. Kelemen, Conditional grammars: motivations, definitions and some properties, In: Proc. Conf. Automata Languages and Math. Sciences, Salgotarjan, 1984, 110–123.

    Google Scholar 

  61. H. C. M. Kleijn, G. Rozenberg, Context-free like restrictions on selective rewriting, Theor. Comp. Sci., 16 (1981), 237–269.

    MathSciNet  MATH  Google Scholar 

  62. S. R. Kosaraju, Decidability of reachability in vector addition systems, In: Proc. 14th Symp. Theory of Computing,1982, 267–281.

    Google Scholar 

  63. J. Kral, A note on grammars with regular restrictions, Kybernetika, 9 (1973), 159–161.

    MathSciNet  MATH  Google Scholar 

  64. W. Kuich, H. A. Maurer, Tuple languages, In: Proc. Intern. Comp. Symp., Bonn, 1970, 881–891.

    Google Scholar 

  65. J. van Leeuwen, The membership question for ETOL systems is polynomially complete, Inform. Proc. Letters, 3 (1975), 138–143.

    MATH  Google Scholar 

  66. J. van Leeuwen (ed.), Handbook of Theoretical Computer Science, Elsevier, Amsterdam, 1994.

    Google Scholar 

  67. I. Litovski, Y. Metivier, Computing with graph rewriting systems with priorities, Theor. Comp. Sci., 115 (1993), 191–224.

    MathSciNet  MATH  Google Scholar 

  68. R. J. Lipton, The reachability problem requires exponential space, Research rep. 62, Yale University, Dept. of Comp. Sci., 1976.

    Google Scholar 

  69. M. K. Levitina, On some grammars with global productions, NTI, Ser. 2, No. 3, (1972), 32–36

    Google Scholar 

  70. A. Manaster Ramer, Uses and misuses of mathematics in linguistics, in: Proc. Xth Congress on Natural and Formal Languages, Sevilla, 1994.

    Google Scholar 

  71. H. A. Maurer, A. Salomaa, D. Wood, Pure grammars, Inform. Control, 42 (1979), 103–141.

    MATH  Google Scholar 

  72. E. W. Mayr, An algorithm for the general Petri net reachability problem, In: Proc. 13th Symp. Theory of Computing,1981, 238–246.

    Google Scholar 

  73. A. Meduna, Generalized forbidding grammars, Intern. J. Computer Math., 36 (1990), 31–38.

    MathSciNet  MATH  Google Scholar 

  74. A. Meduna, Global context-conditional grammars, J. Inform. Process. Cybern., 27 (1991), 159–165.

    MATH  Google Scholar 

  75. A. Meduna, A trivial method of characterizing the family of recursively enumerable languages by scattered context grammars, Bulletin EATCS, 56 (1995), 104–106.

    MATH  Google Scholar 

  76. A. Meduna, Matrix grammars under leftmost and rightmost restriction, In: Mathematical Linguistics and Related Topics ( Gh. Pâun, ed.), Ed. Academiei, Bucharest, 1995, 243–257.

    Google Scholar 

  77. A. Meduna, Syntactic complexity of scattered context grammars, Acta Informatica, 32 (1995), 285–298.

    MathSciNet  MATH  Google Scholar 

  78. A. Meduna, A. Gopalaratnam, On semi-conditional grammars with productions having either forbidding or permitting conditions, Acta Cybernetica, 14 (1994), 307–323.

    MathSciNet  MATH  Google Scholar 

  79. A. Meduna, M. Sarek, C. Crooks, Syntactic complexity of regulated rewriting, Kybernetika, 30 (1994), 177–186.

    MathSciNet  MATH  Google Scholar 

  80. D. Milgram, A. Rosenfeld, A note on scattered context grammars, Inform. Proc. Letters, 1 (1971), 47–50.

    MathSciNet  MATH  Google Scholar 

  81. V. Mitrana, Valence grammars on a free generated group, Bulletin EATCS, 47 (1992), 174–179.

    MATH  Google Scholar 

  82. U. Montanari, Separable graphs, planar graphs and web grammars, Inform. Control, 16 (1970), 243–267.

    MathSciNet  MATH  Google Scholar 

  83. M. Nielsen, EOL systems with control devices, Acta Informatica, 4 (1975), 373–386.

    MATH  Google Scholar 

  84. Gh. Pâun, On the family of finite index matrix languages, J. Comp. Syst. Sci., 18 (1979), 267–280.

    MathSciNet  MATH  Google Scholar 

  85. Gh. Pâun, Some further remarks on the family of finite index matrix languages, RAIRO, Informatique theorique, 13 (1979), 289–297.

    MathSciNet  MATH  Google Scholar 

  86. Gh. Pâun, A new generative device: valence grammars, Rev. Roum. Math. Pures Appl., 25 (1980), 911–924.

    MathSciNet  MATH  Google Scholar 

  87. Gh. Pâun, An infinite hierarchy of matrix languages, Stud. Cerc. Mat., 32 (1980), 697–707.

    MathSciNet  MATH  Google Scholar 

  88. Gh. Pâun, Matrix Grammars (in Romanian), The Scientific and Encyclopaedic Publ. House, Bucharest, 1981.

    Google Scholar 

  89. Gh. Pâun, Six nonterminals are enough for generating each r.e. language by a matrix grammar, Intern. J. Comp. Math., 15 (1984), 23–37.

    MathSciNet  MATH  Google Scholar 

  90. Gh. Pâun, A variant of random context grammars: semi-conditional grammars, Theor. Comp. Sci., 41 (1985), 1–17.

    MATH  Google Scholar 

  91. Gh. Pâun, Some recent restriction in the derivation of context-free grammars, In: Proc. 4th IMYCS, Lecture Notes in Computer Science 281, Springer-Verlag, Berlin, 1986, 96–108.

    Google Scholar 

  92. P. M. Postal, Limitations of phrase structure grammars, In: The Structure of Language: Readings in the Philosophy of Languages ( J. A. Fodor, J. J. Katz, eds.), Prentice-Hall, Englewood Cliffs, N. J., 1964, 137–151.

    Google Scholar 

  93. O. Rambow, Imposing vertical context conditions on derivations, in: Proc. 2nd Conf. Developments in Language Theory, Magdeburg, 1995.

    Google Scholar 

  94. O. Rambow, G. Satta, A rewriting system for natural language syntax that is non-local and mildly context-sensitive, In: Current Issues in Mathematical Linguistics ( C. Martin-Vide, ed.), North-Holland, Amsterdam, 1994, 121–130.

    Google Scholar 

  95. D. Radzinski, Unbounded syntactic copying in Mandarin Chinese, Linguistics and Philosophy, 13 (1990), 113–127.

    Google Scholar 

  96. B. Reichel, A remark on some classifications of Indian parallel languages, in: Machines, Languages and Complexity, Lecture Notes in Computer Science 381, Springer-Verlag, Berlin, 1989, 55–63.

    Google Scholar 

  97. P. J. A. Reusch, Regulierte TOL Systeme, Techn. rep. No. 81, Gesellsch. f. Math. u. Datenverarbeitung, Bonn, 1974.

    Google Scholar 

  98. G. E. Revesz, Introduction to Formal Language Theory, McGraw-Hill, New York, 1983.

    Google Scholar 

  99. D. J. Rosenkrantz, Programmed grammars and classes of formal languages, Journal of the ACM, 16 (1969), 107–131.

    MathSciNet  MATH  Google Scholar 

  100. W. C. Rounds, Complexity of recognition in intermediate-level languages, In: Proc. 14th IEEE Symp. Switching and Automata Theory,1973, 145–158.

    Google Scholar 

  101. G. Rozenberg, A. Salomaa, The Mathematical Theory of L Systems, Academic Press, New York, 1980.

    MATH  Google Scholar 

  102. G. Rozenberg, S. H. von Solms, Some aspects of random context grammars, Informatik-Fachberichte, 5 (1976), 63–75.

    MathSciNet  MATH  Google Scholar 

  103. G. Rozenberg, S. H. von Solms, Priorities on context conditions in rewriting systems, Inform. Sci., 14 (1978), 15–51.

    MathSciNet  MATH  Google Scholar 

  104. G. Rozenberg, D. Vermeir, On the effect of the finite index restriction on several families of grammars I, Inform. Control, 39 (1978), 284–302.

    MathSciNet  MATH  Google Scholar 

  105. G. Rozenberg, D. Vermeir, On the effect of the finite index restriction on several families of grammars II, Found. Control Engineering, 3 (1978), 125–142.

    MATH  Google Scholar 

  106. B. Rozoy, The Dyck language Di* is not generated by any matrix grammar of finite index, Inform. Control, 74 (1987), 64–89.

    MathSciNet  MATH  Google Scholar 

  107. A. Salomaa, Periodically time-variant context-free grammars, Inform. Control, 17 (1970), 294–211.

    MathSciNet  MATH  Google Scholar 

  108. A. Salomaa, Formal Languages, Academic Press, New York, 1973.

    MATH  Google Scholar 

  109. K. Salomaa, Hierarchy of k-context-free languages I, Intern. J. Comp. Math., 26 (1989), 69–90.

    MATH  Google Scholar 

  110. K. Salomaa, Hierarchy of k-context-free languages II, Intern. J. Comp. Math., 26 (1989), 193–205.

    MATH  Google Scholar 

  111. G. Satta, The membership problem for unordered vector languages, in: Proc. 2nd Conf. Developments in Language Theory, Magdeburg, 1995, 267–275.

    Google Scholar 

  112. S. M. Shieber, Evidence against the context-freeness of natural languages, Linguistics and Philosophy, 8 (1985), 333–343.

    Google Scholar 

  113. E. Shamir, C. Beeri, Checking stacks and context-free programmed grammars accept P-complete languages, Lecture Notes Computer Science, 14 Springer-Verlag Berlin, 1974, 27–33.

    Google Scholar 

  114. R. Siromoney, K. Krithivasan, Parallel context-free grammar, Inform. Control, 24 (1974), 155–162.

    MATH  Google Scholar 

  115. S. Skyum, Parallel context-free languages, Inform. Control, 26 (1974), 280–285.

    MathSciNet  MATH  Google Scholar 

  116. S. H. von Solms, Some notes on ETOL languages, Intern. J. Comp. Math., 5 (1976), 285–296.

    MATH  Google Scholar 

  117. S. H. von Solms, Node-label controlled graph grammars with context conditions, Intern. J. Comp. Math., 15 (1984), 39–49.

    MathSciNet  MATH  Google Scholar 

  118. R. Stiebe, Kantengrammatiken, Dissertation, Magdeburg Univ., 1996.

    Google Scholar 

  119. E. D. Stotskij, Remarks on a paper by M. K. Levitina, NTI, Ser. 2, No. 4 (1972), 40–45.

    Google Scholar 

  120. A. P. J. van der Walt, Random context grammars, in: Proc. Symp. on Formal Languages, 1970.

    Google Scholar 

  121. D. Wötjen, k-limited OL systems and languages, J. Inform. Process. Cybern., 24 (1988), 267–288.

    Google Scholar 

  122. D. Wötjen, On k-uniformly-limited TOL systems and languages, J. Inform. Process. Cybern., 26 (1990), 229–238.

    MathSciNet  Google Scholar 

  123. D. Wood, Bicolored digraph grammar systems, RAIRO, Rech. Oper., 1 (1973), 45–50.

    MathSciNet  MATH  Google Scholar 

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  1. Jürgen Dassow
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  2. Gheorghe Păun
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  3. Arto Salomaa
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Editors and Affiliations

  1. Department of Computer Science, Leiden University, P.O. Box 9512, NL-2300 RA, Leiden, The Netherlands

    Grzegorz Rozenberg

  2. Department of Computer Science, University of Colorado at Boulder, Campus 430, 80309, Boulder, CO, USA

    Grzegorz Rozenberg

  3. Turku Centre for Computer Science Data City, FIN-20520, Turku, Finland

    Arto Salomaa

  4. Academy of Finland and Turku Centre for Computer Science (TUCS), Lemninkäisenkatu 14 A, FIN-20520, Turku, Finland

    Arto Salomaa

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Dassow, J., Păun, G., Salomaa, A. (1997). Grammars with Controlled Derivations. In: Rozenberg, G., Salomaa, A. (eds) Handbook of Formal Languages. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-07675-0_3

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