Finite state automata that accepts any string

have already showed that regular language which canвЂ™t be accepted by 1QFA can be accepted by a 2-letter QFA.We continue the investigation of of 1-way quantum finite state automaton and k-letter quantum finite state automaton for improving their language accepting capabilities. In, hierarchy and equivalence of multiletter quantum finite state automaton are studied.Д«elovs et al. further study the decidability of the equivalence and minimization problems of multiletter QFAs. So a k-letter QFA is not limited to see only one,the just incoming input letter. In these model,the automaton is not limited to seeing only one,the just incoming letter, but can see several earlier received letters as well.

In, they proposed a new model of one way QFA, namely, multiletter QFAs, that is an analogue of quantum automaton with classical memory containing the previously read letters. 1-way reversible and multihead finite automaton and 2-way reversible multihead finite automaton are in- troduced as a simple model of reversible computing and its language accepting capability is studied.ДЄ konadacs and J Watrous showed that 1QFA can only recognize regular languages,moreover, 1QFA cannot recognize all the regular languages. Languages accepted by multitape or multihead finite automaton were introduced in and. In, they propose 2-way finite automaton with quantum and classical states, an intermediate model between 1QFAвЂ™s and 2QFAвЂ™s. In this model,it is easy to simulate any deterministic automaton and some non-regular languages can be recognized as well this implies that 2QFAвЂ™s are strictly more powerful than their classical counterparts. The second model is 2-way quantum finite state automaton (2QFA). Nayek proposed a further generalization by allowing the QFA to perform several arbitrary measurements with intermediate unitary trans- formation at each step. Besides these two models of QFA there are also such models of QFA as вЂњenhancedвЂќ quantum finite state automaton, latvian quantum finite state automaton, 1-way QFA with control languages, quantum finite state automaton with quantum and classical states (introduced by aharonov, kitaev and Nisan ). that the languages recognized by 1QFAвЂ™s form a proper subset of the regular languages.

Whenever we mention one-way quantum finite automata we mean the model described by Konadacs et al. Hence, in this paper,we consider the measure many quantum finite automata described by Kondacs et al. showed that measure many one-way quantum finite automata can accept all languages that can be accepted by measure once one-way quantum finite automata. They have seemingly small difference, measure once quantum finite state automaton performs the mea- surement only at the end of computation,but for measure-many quantum finite state automaton the measure- ment will be performed by the automaton at every step of computation. The two most popular models of quantum finite state automaton are quantum finite state automaton introduced by Moore and Crutchfield (measure once quantum finite state automaton) and quan- tum finite state automaton introduced by Kondacs and Watrous (measure many quantum finite state auto- maton). 1-way quantum finite automaton (1QFA) can be seen as the simplest model of quantum automaton. A variety of models of quantum finite state automaton are used.

Likewise a quantum finite state automaton may be seen as basic model of finite state quantum machine. Received 6 April 2016 accepted published Д¬lassical finite state automaton is the very basic model of classical finite machine.

Finite state automata that accepts any string