Insertion systems have a unique feature in that only string insertions are allowed, which is in marked contrast to a variety of the conventional computing devices based on string rewriting. This paper will mainly focus on those systems whose insertion operations are performed in a context-free fashion, called context-free insertion systems, and obtain several characterizations of language families with the help of other primitive languages (like star languages) as well as simple operations (like projections, weak-codings). For each k < 1, a language L is a k-star language if L = F+ for some finite set F with the length of each string in F is no more than k. The results of this kind have already been presented in  by Pun et al., while the purpose of this paper is to prove enhanced versions of them. Specifically, we show that each context-free language L can be represented in the form L = h(L(γ) ∩F+), where γ is an insertion system of weight (3, 0) (at most three symbols are inserted in a context-free manner), h is a projection, and F+ is a 2-star language. A similar characterization can be obtained for recursively enumerable languages, where insertion systems of weight (3, 3) and 2-star languages are involved.
|Number of pages||14|
|Journal||International Journal of Foundations of Computer Science|
|Publication status||Published - Jan 1 2011|
All Science Journal Classification (ASJC) codes
- Computer Science (miscellaneous)