The OI-hierarchy is closed under control

  • Heiko Vogler
Part of the Lecture Notes in Computer Science book series (LNCS, volume 233)


Controlling the derivations of high level grammars by high level languages does not influence their generating power.


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  1. [1]
    A.V. Aho; Indexed grammars, an extension of context-free grammars; JACM 15 (1968), 647–671.Google Scholar
  2. [2]
    P.R.J. Asveld; Controlled iteration grammars and full hyper-AFL's; Inf. and Control 34 (1977), 248–269.Google Scholar
  3. [3]
    P.R.J. Asveld, J. van Leeuwen; Infinite chains of hyper-AFL's; TW-Memorandum 99, Twente University of Technology, Enschede, 1975.Google Scholar
  4. [4]
    K. Culik II; On some families of languages related to develop mental system; Internat. J. Comput. Math. 4 (1974), 31–42.Google Scholar
  5. [5]
    W. Damm; The IO-and OI-hierarchies; TCS 20 (1982), 95–206.Google Scholar
  6. [6]
    W. Damm, A. Goerdt; An automata-theoretic characterization of the OI-hierarchy; Proc. 9th ICALP, 1982, Aarhus, pp. 141–153; to appear in Inf. and Control.Google Scholar
  7. [7]
    J. Duske, R. Parchmann; Linear indexed languages; TCS 32 (1984), 47–60.Google Scholar
  8. [8]
    J. Engelfriet; Surface tree languages and parallel derivation trees; TCS 2 (1976), 9–27.Google Scholar
  9. [9]
    J. Engelfriet; Three hierarchies of transducers; Math. Syst. Theory 15 (1982), 95–125.Google Scholar
  10. [10]
    J. Engelfriet; Iterated pushdown automata and complexity classes; Proc. 15th STOC, April 1983, Boston, pp. 365–373.Google Scholar
  11. [11]
    J. Engelfriet; Context-free grammars with storage; Rep. Nr. 85-, University of Leiden, The Netherlands.Google Scholar
  12. [12]
    J. Engelfriet; The ETOL hierarchy is inside the OI hierarchy; in: "The Book of L" (eds. G. Rozenberg and A. Salomaa), Springer-Verlag, 1986, pp. 101–109.Google Scholar
  13. [13]
    J. Engelfriet, G. Rozenberg, G. Slutzki; Tree transducers, L-systems, and two-way machines; JCSS 20 (1980), 150–202.Google Scholar
  14. [14]
    J. Engelfriet, E.M. Schmidt; IO and OI; JCSS 15 (1977), 328–353 and JCSS 16 (1978), 67–99.Google Scholar
  15. [15]
    J. Engelfriet, H. Vogler; Pushdown machines for the macro tree transducer; Rep. Nr. 84-13, University of Leiden, The Netherlands, 1984.Google Scholar
  16. [16]
    J. Engelfriet, H. Vogler; High level tree transducers and iterated pushdown machines; Rep. Nr. 85-12, University of Leiden, The Netherlands, 1985.Google Scholar
  17. [17]
    M.J. Fischer; Grammars with macro-like productions; Ph. D. Thesis, Harvard University, USA, 1968.Google Scholar
  18. [18]
    S. Ginsburg, G. Rozenberg; TOL schemes and control sets; Inf. and Control 27 (1975), 109–125.Google Scholar
  19. [19]
    S. Ginsburg, E. H. Spanier; Control sets on grammars; Math. Syst. Theory 2 (1968), 159–177.Google Scholar
  20. [20]
    S.A. Greibach; Full AFLs and nested iterated substitution; Inf. and Contr. 16 (1970), 7–35.Google Scholar
  21. [21]
    S.A. Greibach; Control sets on context-free grammar forms; JCSS 15 (1977), 35–98.Google Scholar
  22. [22]
    J.E. Hopcroft, J.D. Ullman; "Introduction to Automata Theory, Languages, and Computation"; Addison-Wesley Publ. Comp., Reading, Mass., 1978.Google Scholar
  23. [23]
    N.A. Khabbaz; A geometric hierarchy of languages; JCSS 8 (1974), 206–221.Google Scholar
  24. [24]
    N.A. Khabbaz; Control sets on linear grammars; Inf. and Contr. 25 (1974), 206–221.Google Scholar
  25. [25]
    K.-J. Lange; Context-free controlled ETOL systems, Proc. 10th ICALP (ed. J. Diaz), LNCS 154, Springer-Verlag, 1983, 723–733.Google Scholar
  26. [26]
    G. Rozenberg; Extension of tabled OL-systems and languages; Internat. J. Comp. Inform. Sci. 2 (1973), 311–336.Google Scholar
  27. [27]
    A. Salomma; "Formal Languages", Academic Press, New York, 1973.Google Scholar
  28. [28]
    J. van Leeuwen; Variations of a new machine model; 17th Ann. IEEE Symp. on Foundations of Computer Science, Houston, 1976.Google Scholar
  29. [29]
    H. Vogler; Iterated linear control and iterated one-turn pushdowns; Rep. Nr. 85-04, University of Leiden, The Netherlands, 1985. See also: Proc. 5th FCT.Google Scholar
  30. [30]
    M. Wand; An algebraic formulation of the Chomsky-hierarchy, Cate-Springer, Berlin, 1975, p. 209–213.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Heiko Vogler
    • 1
  1. 1.University of LeidenThe Netherlands

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