A generalization of the Parikh vector for finite and infinite words

  • Rani Siromoney
  • V. Rajkumar Dare
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 206)


A metric is defined on the set of all finite and infinite words based on the difference between the occurrences of different letters of the alphabet. This induces a topology which coincides with the metric topology defined by Nivat [5]. Using this metric a vector is defined which gives rise to the position vector p showing the position in the word of each letter of the alphabet. The p-vector can be regarded as a generalization of the Parikh vector [6]. While the Parikh vector of a word enumerates the number of occurrences of each letter of the alphabet, the p-vector introduced in this paper indicates the positions of each letter of the alphabet in the word. Also, the Parikh vector is defined for finite words and the p-vector gives a generalization to infite words. The p-vector has nice mathematical properties. Characterizations of regular sets, context-free languages and a few families from Lindenmayer systems are given.


Position Vector Regular Language Formal Language Theory Infinite Word Binary Alphabet 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1985

Authors and Affiliations

  • Rani Siromoney
    • 1
  • V. Rajkumar Dare
    • 1
  1. 1.Department of MathematicsMadras Christian CollegeTambaram, Madras

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