On the power of two-way multihead quantum finite automata

This paper introduces a variant of two-way quantum finite automata named two-way multihead quantum finite automata. A two-way quantum finite automaton is more powerful than classical two-way finite automata. However, the generalizations of two-way quantum finite automata have not been defined so far as compared to one-way quantum finite automata model. We have investigated the newly introduced automata from two aspects: the language recognition capability and its comparison with classical and quantum counterparts. It has been proved that a language which cannot be recognized by any one-way and multi-letter quantum finite automata can be recognized by two-way quantum finite automata. Further, it has been shown that a language which cannot be recognized by two-way quantum finite automata can be recognized by two-way multihead quantum finite automata with two heads. Furthermore, it has been investigated that quantum variant of two-way deterministic multihead finite automata takes less number of heads to recognize a language containing of all words whose length is a prime number.