Language equations, maximality and error-detection

We use some ‘natural’ language operations, such as shuffle (scattered insertion) and scattered deletion to model 9 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 11 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 13 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 15 code of the type defined by the inequation is maximal. © 2004 Published by Elsevier Inc. 17