Abstract
The 1-way quantum finite automata and 2-way quantum finite automata are the first ever developed quantum automatons. But they suffer from many disadvantages which make them less powerful and impracticable. To remove these drawbacks there are many ways to modify and aggrandize the quantum finite automatons. Including 1-counter with 1-way QFA significantly improve its power. Likely quantum finite automata with quantum and classical states (QCFA) and 2-way quantum finite 1-counter automata (2-QF1-CA) are the quintessence of these modifications. In our paper we first discuss about 1-QFA and 2-QFA and their drawbacks. In the section IV we introduce an algorithm by implementing 1-way quantum finite k-counter automata (1-QFk-CA). Then we discuss another algorithm by implementing quantum finite 1-counter automata (QF1-CA) with multiple scanning of the input string. These algorithms improve the power of QFAs.
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