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)


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.


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.


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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

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