MORPHIC CHARACTERIZATIONS OF LANGUAGE FAMILIES IN TERMS OF INSERTION SYSTEMS AND STAR LANGUAGES

FUMIYA OKUBO, TAKASHI YOKOMORI
2011 International Journal of Foundations of Computer Science  
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
more » ... 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 [10] by Pȃun 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.
doi:10.1142/s012905411100799x fatcat:6gyge2dnnrhu3jfm3fmgz32g54