Hairpin finite automata

We introduce and investigate nondeterministic finite automata with the additional ability to apply the hairpin inversion operation to the remaining part of the input. We consider three different modes of hairpin operations, namely left-most hairpin, general hairpin, and right-most hairpin. We show that these operations do not increase the computation power, when the number of operations is bounded by a constant. An unbounded number of these operations leads to language families that are properly contained in the family of context-sensitive languages and are supersets of the family of regular languages. Moreover, we show that in most cases we obtain incomparability results for the language families under consideration. Finally, we summarize closure properties of language families accepted by variants of hairpin finite automata.