Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A word rewriting system is called monadic if each of its right hand sides is either a single letter or the empty word.  study the images of higher order indexed languages (defined by Maslov) under inverse derivations of infinite monadic systems.  show that the inverse derivations of deterministic level n indexed languages by confluent regular monadic systems are deterministic level n+1 languages, and that the inverse derivations of level n indexed monadic systems preserve level $n$ indexed languages. Both results are established using a fine structural study of classes of infinite automata accepting level $n$ indexed languages. Our work generalizes formerly known results about regular and context-free languages which form the first two levels of the indexed language hierarchy.
['Didier Caucal', 'Teodor Knapik']
I am writing a research paper on a idea Higher order indexed monadic systems
[{"from": "human", "value": "I am writing a research paper on a idea Higher order indexed monadic systems"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: A word rewriting system is called monadic if each of its right hand sides is either a single letter or the empty word.  study the images of higher order indexed languages (defined by Maslov) under inverse derivations of infinite monadic systems.  show that the inverse derivations of deterministic level n indexed languages by confluent regular monadic systems are deterministic level n+1 languages, and that the inverse derivations of level n indexed monadic systems preserve level $n$ indexed languages. Both results are established using a fine structural study of classes of infinite automata accepting level $n$ indexed languages. Our work generalizes formerly known results about regular and context-free languages which form the first two levels of the indexed language hierarchy."}]