Closure and decidability properties of some language classes with respect to ciliate bio-operations

  • Authors:

  • Mark Daley;Oscar H. Ibarra;Lila Kari

  • Affiliations:

  • Department of Computer Science, University of Western Ontario, London, Canada ON N6A 5B7;Department of Computer Science, University of California, Santa Barbara, CA;Department of Computer Science, University of Western Ontario, London, Canada ON N6A 5B7

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2003

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Abstract

The process of gene unscrambling in ciliates (a type of unicellular protozoa), which accomplishes the difficult task of re-arranging gene segments in the correct order and deleting non-coding sequences from an "encrypted" version of a DNA strand, has been modeled and studied so far from the point of view of the computational power of the DNA bio-operations involved. Here we concentrate on a different aspect of the process, by considering only the linear version of the bio-operations, that do not involve thus any circular strands, and by studying the resulting formal operations from a purely language-theoretic point of view. We investigate closure properties of language families under the mentioned bio-operations and study language equations involving them. We also study the decidability of the existence of solutions to equations of the form L ♦ Y = R, X ♦ L = R where L and R are given languages, X and Y are unknowns, and ♦ signifies one of the defined bio-operations.