Restricted Insertion-Deletion Systems

In the past few years several paper showed, that various generative mechanisms in formal language theory that used context-dependent insertions and deletions are capable of generating any recursively enumerable languages [1, 2, 3, 4, 5, 6, 7, 8, 9]. Since such systems are also models of molecular computing, for practical reasons it is important to examine these systems in a restricted case, in which the number of symbols in the model of the alphabet is limited. In [4] it is showed that we can define the generated language of an insertion-deletion system in such a way, that a two-letter alphabet is enough to generate any recursively enumerable language. In this paper we complete this result by showing that the same generative capacity can be obtained even if we define the generated language the traditional way.