Correlations of Partial Words

  • Francine Blanchet-Sadri
  • Joshua D. Gafni
  • Kevin H. Wilson
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4393)

Abstract

Partial words are strings over a finite alphabet that may contain a number of “do not know” symbols. In this paper, we introduce the notions of binary and ternary correlations, which are binary and ternary vectors indicating the periods and weak periods of partial words. Extending a result of Guibas and Odlyzko, we characterize precisely which of these vectors represent the (weak) period sets of partial words and prove that all valid correlations may be taken over the binary alphabet. We show that the sets of all such vectors of a given length form distributive lattices under inclusion. We also show that there is a well defined minimal set of generators for any binary correlation of length n and demonstrate that these generating sets are the primitive subsets of {1, 2,..., n − 1}. Finally, we investigate the number of correlations of length n.

Keywords

Partial Word Valid Correlation Null Element Universal Element Binary Alphabet 
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 Berlin Heidelberg 2007

Authors and Affiliations

  • Francine Blanchet-Sadri
    • 1
  • Joshua D. Gafni
    • 2
  • Kevin H. Wilson
    • 3
  1. 1.Department of Computer Science, University of North Carolina, P.O. Box 26170, Greensboro, NC 27402–6170USA
  2. 2.Department of Mathematics, University of Pennsylvania, Philadelphia, PA 19104–6395USA
  3. 3.Department of Mathematics, University of Michigan, Ann Arbor, MI 48109–1043USA

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