Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Two-way finite automata with quantum and classical states (2QCFA) re introduced by Ambainis and Watrous, and it was shown that 2QCFA have superiority over two-way probabilistic finite automata (2PFA) for recognizing some non-regular languages such as the language Leq = {anbn ∣ n ∈ N} and the palindrome language Lpal = {w ∈ {a,b}* ∣ w=wR}, where xR is x in the reverse order. It is interesting to find more languages like these that witness the superiority of 2QCFA over 2PFA. ,  consider the language Lm = {xcy ∣ ∑ = {a,b,c},x,y ∈ {a,b}*, ∣x∣ = ∣y∣} that is similar to the middle language Lmiddle = {xay ∣ x,y ∈ {a,b}*, ∣x∣ = ∣y∣}.  prove that the language Lm show that Lm can be recognized by 2PFA with bounded error, but only in exponential expected time. Thus Lm is another witness of the fact that 2QCFA are more porful than their classical counterparts.
['Shenggen Zheng', 'Daowen Qiu', 'Lvzhou Li']
I am writing a research paper on a idea Some Languages Recognized by Two-Way Finite Automata with Quantum and Classical States
[{"from": "human", "value": "I am writing a research paper on a idea Some Languages Recognized by Two-Way Finite Automata with Quantum and Classical States"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Two-way finite automata with quantum and classical states (2QCFA) re introduced by Ambainis and Watrous, and it was shown that 2QCFA have superiority over two-way probabilistic finite automata (2PFA) for recognizing some non-regular languages such as the language Leq = {anbn \u2223 n \u2208 N} and the palindrome language Lpal = {w \u2208 {a,b}* \u2223 w=wR}, where xR is x in the reverse order. It is interesting to find more languages like these that witness the superiority of 2QCFA over 2PFA. ,  consider the language Lm = {xcy \u2223 \u2211 = {a,b,c},x,y \u2208 {a,b}*, \u2223x\u2223 = \u2223y\u2223} that is similar to the middle language Lmiddle = {xay \u2223 x,y \u2208 {a,b}*, \u2223x\u2223 = \u2223y\u2223}.  prove that the language Lm show that Lm can be recognized by 2PFA with bounded error, but only in exponential expected time. Thus Lm is another witness of the fact that 2QCFA are more porful than their classical counterparts."}]