Advertisement

Initial index: A new complexity function for languages

  • J. Gabarro
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 154)

Abstract

A new complexity measure for languages is defined, called the initial index. This measure is of combinatorial nature; it is a function defined by counting the minimal number of states of automata recognizing approximations of a language.

The family of polynomial initial languages is defined, and it is proved that it is an intersection-closed A.F.L. The relations between this family and on-line multicounter Turing-machines, Petri-net languages and context-free languages are investigated. The family of exponential initial index languages is defined. The relations of this family with generators of usual families under usual operations are studied. At the end of the paper we relate the initial index with other complexity measures such as growth functions, rational index and straight-line programs.

Keywords

Rational Index Complexity Measure Growth Function Derivation Tree Deterministic Automaton 
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. [1]
    Berstel, J. [1979]. “Transductions and Context free languages”, Teubner Studienbücher, Stuttgart.Google Scholar
  2. [2]
    Boasson, L. [1971]. “Cones rationnels et familles agreables de langages — application aux langages a compteur”. Thèse de 3ème cycle. Paris VII.Google Scholar
  3. [3]
    Boasson, L; B. Courcelle; M. Nivat [1981]. “The rational index a complexity measure for languages”. SIAM Journal on computing 10, 2, 284–296.Google Scholar
  4. [4]
    Book, R. [1982]. “Intersection of CFL's and related structures” in Actes de l'école de printemps de théorie de langages. Editeur Blab. M. publication of LITP nℴ 82-14.Google Scholar
  5. [5]
    Bucher. W; K. Culik; H. Maurer; D. Wotschke. “Concise description of finite languages”. Theor. Comput. Sci. 14, 3, 211–347 (1981).Google Scholar
  6. [6]
    Culik II. K; H.A. Maurer. “On the derivation trees”. Internal report.Google Scholar
  7. [7]
    Crespi-Reghizzi, S.; D. Mandrioli [1977] “Petri nets and Szilard languages”, Inf. and Control, 33, 177–192.Google Scholar
  8. [8]
    Deleage, J.L. [1982]. “Memoire de D.E.A.”, Paris VII, unpublihed manuscript.Google Scholar
  9. [9]
    Fischer, P.C.; A.R. Meyer; A.L. Rosenberg [1968], Math. Syst. Theor.2. 3, 265.Google Scholar
  10. [10]
    Gabarro, J. [1982]. “Une application des notions de centre et index rationnel à certains langages algébriques”. RAIRO Inf. Theor. 16, 4, 317–329.Google Scholar
  11. [11]
    Ginsburg, S.; Greibach, S. [1969]. “Abstract families of languages” in Abstract families of languages. Mem. of the Amer. Math. Soc. 87, 1–32.Google Scholar
  12. [12]
    Goodrich, G.B.; Ladner, R.E.; Fischer, M. J. [1977]. “Straight-Line programs to compute finite languages”, A conference on Theorethical Computer Science, Aug. 1977, Waterloo, Canada.Google Scholar
  13. [13]
    Greibach, S.A. [1976]. Remarks on the complexity of non deterministic counter languages”, Theor. Comput. Sci. 1, 269–288.Google Scholar
  14. [14]
    Greibach, S.A. [1978]. Remarks on blind and partially blind one-way multicounter machines”, Theor. Comput. Sci. 7, 311–324.Google Scholar
  15. [15]
    Hack, M. [1975]. “Petri nets languages”, Computation Structures Group Memo 124, Project MAC, MIT Cambridge, Mass.Google Scholar
  16. [16]
    Jantzen, M. [1973]. “One hierarchy of Petri net languages”, RAIRO Inf. Theor. 13, 1, 19–30.Google Scholar
  17. [17]
    Knuth, D.E. [1976]. “Big omicron and big omega and big theta”. Sigact News Apr–June 18–24.Google Scholar
  18. [18]
    Milnor, J. [1968]. “A note on curvature and fundamental group”, J. Differential Geometry 2, 1–7.Google Scholar
  19. [19]
    Nivat, M. [1968]. “Transductions des langages de Chomsky”. Ann. de 1'Ins t. Fourier 18, 339–456.Google Scholar
  20. [20]
    Paredaens, J.; R. Vyncke [1977]. “A class of measure on formal languages”. Acta Informatica, I, 73–86.Google Scholar
  21. [21]
    Peterson, J.L. [1976]. “Computations sequence sets”, J. Comput. and Syst. Sci. 13, 1, 1–24.Google Scholar
  22. [22]
    Savage, J.E. 1972. “Computational work and time on Finite Machines”. J.A.C.M. 19, 4, 660–674.Google Scholar
  23. [23]
    Trofimov, V.I. [1980]. “The growth function of finitely generated semigroup”, Semigroup Forum 21, 351–360.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1983

Authors and Affiliations

  • J. Gabarro
    • 1
  1. 1.L.I.T.P. et Université Pierre et Marie CurieParis Cedex 05France

Personalised recommendations