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Language families defined by a ciliate bio-operation: hierarchies and decision problems

We formalize the hairpin inverted repeat excision, which is known in ciliate genetics as an operation on words and languages by defining as the set of all words xαyRαRz where w = xαyαRz and the pointer α is in P. We extend this concept to language families which results in families . For and be the families of finite, regular, context-free, context-sensitive or recursively enumerable language, respectively, we determine the hierarchy of the families and compare these families with those of the Chomsky hierarchy. Furthermore, we present the status of decidability of the membership problem, emptiness problem and finiteness problem for the families .