A ciliate bio-operation and language families

Abstract

We formalize the hairpin inverted repeat operation, which is known in ciliate genetics as an operation on words and languages by defining ℋℐ(w,P) as the set of all words xαyRα Rz where w = xαyαRz and the pointer α is in P. We extend this concept to language families which results in families ℋℐ(ℒ1,ℒ2). For L1 and L2 being the families of finite, regular, context-free, context-sensitive or recursively enumerable language, respectively, we determine the hierarchy of the families ℋℐ(ℒ1, ℒ2) and compare these families with those of the Chomsky hierarchy. Furthermore, we give some results on the decidability of the membership problem, emptiness problem and finiteness problem for the families ℋℐ(ℒ1, ℒ2). © Springer-Verlag Berlin Heidelberg 2004.