Advertisement

An automata-theoretic characterization of the OI-hierarchy

  • Werner Damm
  • Andreas Goerdt
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 140)

Abstract

Though is was “obvious” to “insiders”, that the level-n pds — which circulated in unformalized versions prior to the knowledge of Maslov's papers — just had to be the automata model fitting to level-n languages, the complexity of the encodings in both directions shows, how far apart both concepts are. We hope that the technics develloped in establishing
$$\frac{{5.1{\text{}}Theorem}}{{\forall \Omega {\text{ }} \geqslant {\text{ }}1}}{\text{ }}n - L_{OI} {\text{ (}}\sum {\text{) = n}} - \mathcal{P}\mathcal{D}\mathcal{A}{\text{ (}}\sum {\text{)}}$$
will turn out to be useful in further applications, e.g. reducing the equivalence problem of level-n schemes [Da 1] to that of deterministic n-pda's (c.f. [Cou], [Gal] for the case n=1).

Keywords

Sentential Form Deterministic Finite Automaton Inductive Definition Applicative Term Start Symbol 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. [Aho]
    AHO, A.V. Nested stack automata, JACM 16, 3 (1969), 383–406MathSciNetCrossRefGoogle Scholar
  2. [BD]
    BILSTEIN, J. / DAMM, W. Top-down tree-transducers for infinite trees I, Proc. 6th CAAP, LNCS 112 (1981), 117–134MathSciNetzbMATHGoogle Scholar
  3. [Cou]
    COURCELLE, B. A representation of trees by languages, TCS 6, (1978), 255–279 and 7, (1978), 25–55MathSciNetCrossRefGoogle Scholar
  4. [Da 1]
    DAMM, W. The IO-and OI-hierarchies, TCS 20, (1982), to appearMathSciNetCrossRefGoogle Scholar
  5. [Da 2]
    DAMM, W. An algebraic extension of the Chomsky-hierarchy, Proc. MFCS'79, LNCS 74 (1979), 266–276zbMATHGoogle Scholar
  6. [DF]
    DAMM, W. / FEHR, E. A schematalogical approach to the analysis of the procedure concept in ALGOL-languages, Proc. 5th CAAP, Lille, (1980), 130–134Google Scholar
  7. [DGu]
    DAMM, W. / GUESSARIAN, I. Combining T and level-N, Proc. MFCS'81, LNCS 118 (1981), 262–270zbMATHGoogle Scholar
  8. [ES]
    ENGELFRIET, J. / SCHMIDT, E.M. IO and OI, JCSS 15, 3 (1977), 328–353 and JCSS 16, 1 (1978), 67–99MathSciNetzbMATHGoogle Scholar
  9. [Fi]
    FISCHER, M.F. Grammare with macro-like productions, Proc. 9th SWAT, (1968), 131–142Google Scholar
  10. [Gal]
    GALLIER, J.H. Deterministic finite automata with recursive calls and DPDA's technical report. University of Pennsylvania, (1981)Google Scholar
  11. [Goe 1]
    GOERDT, A. Eine automatentheoretische Charakterisierung der OI-Hievarchie, to appearGoogle Scholar
  12. [Goe 2]
    GOERDT, A. Characterizing generalized indexed languages by n-pda's Schriften zur Informatik und Angewandten Mathematik, RWTH Aachen, to appearGoogle Scholar
  13. [Gre]
    GREIBACH, S.A. Full AFL's and nested iterated Substitution, Information and Control 16, 1 (1970), 7–35MathSciNetCrossRefGoogle Scholar
  14. [Kle]
    KLEIN, H.-J. personal communicationGoogle Scholar
  15. [Kot]
    KOTT, L. Sémantique algébrique d'un langage de programmation type ALGOL RAIRO 11, 3 (1977), 237–263MathSciNetzbMATHGoogle Scholar
  16. [Mas]
    MASLOV, A.N. Multilevel stack automata, Problemy Peredachi Informatsii 12, 1 (1976), 55–62MathSciNetGoogle Scholar
  17. [PDS]
    PARCHMANN, R. / DUSKE, J. / SPECHT, J. On deterministic indexed languages, Information and Control 45, 1 (1980), 48–67MathSciNetCrossRefGoogle Scholar
  18. [Wa]
    WAND, M. An algebraic formulation of the Chomsky-hierarchy, Category Theory Applied to Computation and Control, LNCS 25 (1975), 209–213MathSciNetCrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1982

Authors and Affiliations

  • Werner Damm
    • 1
  • Andreas Goerdt
    • 1
  1. 1.Lehrstuhl für Informatik IIRWTH AachenDeutschland

Personalised recommendations