Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the relations beten the notions of highness, lowness and logical depth in the setting of complexity theory.  introduce a new notion of polynomial depth based on time bounded Kolmogorov complexity.  show our polynomial depth notion satisfies all basic logical depth properties, namely neither sets in P nor sets random for EXP are polynomial deep, and only polynomial deep sets can polynomially Turing compute a polynomial deep set.  prove all EXP- complete sets are poly-deep, and under the assumption that NP does not have p-measure zero, then NP contains a polynomial deep set.  show that every high set for E contains a polynomial deep set in its polynomial Turing degree, and that there exists low for E polynomial deep sets.
['Philippe Moser']
I am writing a research paper on a idea Polynomial Depth, Highness and Lowness for E
[{"from": "human", "value": "I am writing a research paper on a idea Polynomial Depth, Highness and Lowness for E"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the relations beten the notions of highness, lowness and logical depth in the setting of complexity theory.  introduce a new notion of polynomial depth based on time bounded Kolmogorov complexity.  show our polynomial depth notion satisfies all basic logical depth properties, namely neither sets in P nor sets random for EXP are polynomial deep, and only polynomial deep sets can polynomially Turing compute a polynomial deep set.  prove all EXP- complete sets are poly-deep, and under the assumption that NP does not have p-measure zero, then NP contains a polynomial deep set.  show that every high set for E contains a polynomial deep set in its polynomial Turing degree, and that there exists low for E polynomial deep sets."}]