Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Our motivating question is a My hill-Nerode theorem for infinite alphabets.  consider several kinds of those: alphabets whose letters can be compared only for equality, but also ones with more structure, such as a total order or a partial order.  develop a framework for studying such alphabets, where the key role is played by the automorphism group of the alphabet. This framework builds on the idea of nominal sets of Gabbay and Pitts, nominal sets are the special case of our framework where letters can be only compared for equality.  use the framework to uniformly generalize to infinite alphabets parts of automata theory, including decidability results. In the case of letters compared for equality,  obtain automata equivalent in expressive por to finite memory automata, as defined by Francez and Kaminski.
['Mikołaj Bojańczyk', 'Bartek Klin', 'Sławomir Lasota']
I am writing a research paper on a idea Automata with Group Actions
[{"from": "human", "value": "I am writing a research paper on a idea Automata with Group Actions"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Our motivating question is a My hill-Nerode theorem for infinite alphabets.  consider several kinds of those: alphabets whose letters can be compared only for equality, but also ones with more structure, such as a total order or a partial order.  develop a framework for studying such alphabets, where the key role is played by the automorphism group of the alphabet. This framework builds on the idea of nominal sets of Gabbay and Pitts, nominal sets are the special case of our framework where letters can be only compared for equality.  use the framework to uniformly generalize to infinite alphabets parts of automata theory, including decidability results. In the case of letters compared for equality,  obtain automata equivalent in expressive por to finite memory automata, as defined by Francez and Kaminski."}]