Colloquium on Trees in Algebra and Programming

CAAP 1994: Trees in Algebra and Programming — CAAP'94 pp 130-141

Generalizations of the periodicity theorem of Fine and Wilf

  • R. Giancarlo
  • F. Mignosi
Contributed Papers

DOI: 10.1007/BFb0017478

Volume 787 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Giancarlo R., Mignosi F. (1994) Generalizations of the periodicity theorem of Fine and Wilf. In: Tison S. (eds) Trees in Algebra and Programming — CAAP'94. CAAP 1994. Lecture Notes in Computer Science, vol 787. Springer, Berlin, Heidelberg

Abstract

We provide three generalizations to the two-dimensional case of the well known periodicity theorem by Fine and Wilf [4] for strings (the one-dimensional case). The first and the second generalizations can be further extended to hold in the more general setting of Cayley graphs of groups. Weak forms of two of our results have been developed for the design of efficient algorithms for two-dimensional pattern matching [2, 3, 6].

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Copyright information

© Springer-Verlag 1994

Authors and Affiliations

  • R. Giancarlo
    • 1
  • F. Mignosi
    • 2
  1. 1.AT&T Bell LaboratoriesMurray HillUSA
  2. 2.Dipartimento di Matematica ed ApplicazioniUniversitá di PalermoItalia