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

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 LlozengeY=R, XlozengeL=R where L and R are given languages, X and Y are unknowns, and lozenge signifies one of the defined bio-operations. (C) 2003 Elsevier B.V. All rights reserved.