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Algorithms for Factorizing and Testing Subsemigroups

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Combinatorial Algorithms on Words

Part of the book series: NATO ASI Series ((NATO ASI F,volume 12))

Abstract

Given a finite subset Γ of a fixed, finite alphabet Σ, we construct the basis B of the minimum subsemigroup of Σ+ containing Γ, such that B has various properties. The properties we consider are that B be a uniquely decipherable, a finitely decipherable, a synchronizable, or a prefix code. The algorithm for constructing the uniquely decipherable and the finitely decipherable code B requires O(n 2 L + L 2) steps, the algorithm for constructing the synchronizable code B requires O(n L 2) steps, and the algorithm for constructing the prefix code B requires O(L 2) steps. Here n is the cardinality of Γ and L is the sum of the lengths of the words in Γ. Finally, given a synchronizable or finitely decipherable code Γ, we also show how to determine its synchronizability or decipherability delay, in O(n L) steps.

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Author information

Authors and Affiliations

  1. Dipartimento di Informatica ed Applicazioni, Universitá di Salerno, Salerno, 84100, Italy

    Renato M. Capocelli

  2. Department of Computer Science, Purdue University, West Lafayette, Ind., 47907, USA

    Christoph M. Hoffmann

Authors
  1. Renato M. Capocelli
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  2. Christoph M. Hoffmann
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Editor information

Editors and Affiliations

  1. Department of Computer Sciences, Mathematical Sciences Building, 47906, West Lafayette, IN, USA

    Alberto Apostolico

  2. Department of Computer Science, Columbia University, 10027, New York, NY, USA

    Zvi Galil

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© 1985 Springer-Verlag Berlin Heidelberg

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Capocelli, R.M., Hoffmann, C.M. (1985). Algorithms for Factorizing and Testing Subsemigroups. In: Apostolico, A., Galil, Z. (eds) Combinatorial Algorithms on Words. NATO ASI Series, vol 12. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-82456-2_5

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  • DOI: https://doi.org/10.1007/978-3-642-82456-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-82458-6

  • Online ISBN: 978-3-642-82456-2

  • eBook Packages: Springer Book Archive

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