Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove a pumping lemma in order to characterize the infinite words determined by indexed languages. An infinite language L determines an infinite word α if every string in L is a prefix of α. If L is regular or context-free, it is known that α must be ultimately periodic.  show that if L is an indexed language, then α is a morphic word, i.e., α can be generated by iterating a morphism under a coding. Since the other direction, that every morphic word is determined by some indexed language, also holds, this implies that the infinite words determined by indexed languages are exactly the morphic words. The pumping lemma which  use to obtain this result generalizes one recently proved for the class ET0L.
['Tim Smith']
I am writing a research paper on a idea A new pumping lemma for indexed languages, with an application to infinite words
[{"from": "human", "value": "I am writing a research paper on a idea A new pumping lemma for indexed languages, with an application to infinite words"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  prove a pumping lemma in order to characterize the infinite words determined by indexed languages. An infinite language L determines an infinite word \u03b1 if every string in L is a prefix of \u03b1. If L is regular or context-free, it is known that \u03b1 must be ultimately periodic.  show that if L is an indexed language, then \u03b1 is a morphic word, i.e., \u03b1 can be generated by iterating a morphism under a coding. Since the other direction, that every morphic word is determined by some indexed language, also holds, this implies that the infinite words determined by indexed languages are exactly the morphic words. The pumping lemma which  use to obtain this result generalizes one recently proved for the class ET0L."}]