Language equations, maximality and error-detection

  • Authors:

  • Lila Kari;Stavros Konstantinidis

  • Affiliations:

  • Department of Computer Science, University of Western Ontario, London, Ont., Canada N6A 5B7;Department of Mathematics and Computing Science, Saint Mary's University, Halifax, NS, Canada B3H 3C3

  • Venue:
  • Journal of Computer and System Sciences
  • Year:
  • 2005

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Abstract

We use some 'natural' language operations, such as shuffle (scattered insertion) and scattered deletion to model noisy channels, that is, nondeterministic processes transforming words to words. In this spirit, we also introduce the operation of scattered substitution and derive the closure properties of the language families in the Chomsky hierarchy under this operation. Moreover, we consider a certain type of language inequations involving language operations and observe that, by varying the parameters of such an inequation, we can define families of codes such as prefix and infix, as well as families of error-detecting languages. Our results on this type of inequations include a characterization of the maximal solutions, which provides a uniform method for deciding whether a given regular code of the type defined by the inequation is maximal.