A Ciliate Bio-operation and Language Families

Abstract

AbstractWe formalize the hairpin inverted repeat operation, which is known in ciliate genetics as an operation on words and languages by defining \(\mathcal{HI}(w, P)\) as the set of all words xα y R α R z where w = xα yα R z and the pointer α is in P. We extend this concept to language families which results in families \(\mathcal{HI}(L_{1},L_{2})\). For L 1 and L 2 being the families of finite, regular, context-free, context-sensitive or recursively enumerable language, respectively, we determine the hierarchy of the families \(\mathcal{HI}(L_{1},L_{2})\) 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 \(\mathcal{HI}(L_{1},L_{2})\).KeywordsFormal LanguageRegular LanguageClosure PropertyDouble LoopLanguage FamilyThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.