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Initial index: A new complexity function for languages

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Automata, Languages and Programming (ICALP 1983)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 154))

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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.

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Authors and Affiliations

  1. L.I.T.P. et Université Pierre et Marie Curie, U.E.R. 50, Tour 55-65 4, Place Jussieu, 75230, Paris Cedex 05, France

    J. Gabarro

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  1. J. Gabarro
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Josep Diaz

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© 1983 Springer-Verlag Berlin Heidelberg

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Gabarro, J. (1983). Initial index: A new complexity function for languages. In: Diaz, J. (eds) Automata, Languages and Programming. ICALP 1983. Lecture Notes in Computer Science, vol 154. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0036911

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  • DOI: https://doi.org/10.1007/BFb0036911

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12317-0

  • Online ISBN: 978-3-540-40038-7

  • eBook Packages: Springer Book Archive

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