Some Remarks on Superposition Based on Watson-Crick-Like Complementarity

In this note we solve a problem left open in [2]: namely, we show that the iterated superposition of a regular language is regular. The proof of this result is based on two facts: (i) the iterated superposition of a language equals the restricted iterated superposition of the same language, (ii) the sequence formed by iteratively applying the restricted superposition can be precisely defined. We then define the restricted superposition distance between a word and a language and prove that this distance can be computed in time O(nf(n)), where the language is accepted in time O(f(n)) in the RAM model. Finally, we briefly discuss the necessity of the n factor for the classes of regular and context-free languages.