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Counting Finite Languages by Total Word Length

Stefan Gerhold
Published Online: 2011-08-04 | DOI: https://doi.org/10.1515/INTEG.2011.068


We investigate the number of sets of words that can be formed from a finite alphabet, counted by the total length of the words in the set. An explicit expression for the counting sequence is derived from the generating function, and asymptotics for large alphabet size and large total word length are discussed. Moreover, we derive a Gaussian limit law for the number of words in a random finite language.

Keywords.: Finite Languages; Saddle Point Method

About the article

Received: 2010-11-16

Revised: 2011-04-05

Accepted: 2011-04-28

Published Online: 2011-08-04

Published in Print: 2011-12-01

Citation Information: Integers, Volume 11, Issue 6, Pages 863–872, ISSN (Print) 1867-0652, DOI: https://doi.org/10.1515/INTEG.2011.068.

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