Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  investigate in a method for proving separation results for abstract classes of languages. A ll established method to characterize varieties of regular languages are identities.  use a recently established generalization of these identities to non-regular languages by Gehrke, Grigorieff, and Pin: so called equations, which are capable of describing arbitrary Boolean algebras of languages. #R##N#While the main concern of their result is the existence of these equations,  investigate in a general method that could allow to find equations for language classes in an inductive manner. #R##N#Thereto  extend an important tool -- the block product or substitution principle -- known from logic and algebra, to non-regular language classes. Furthermore,  abstract this concept by defining it directly as an operation on (non-regular) language classes.  show that this principle can be used to obtain equations for certain circuit classes, given equations for the gate types. #R##N#Concretely,  demonstrate the applicability of this method by obtaining a description via equations for all languages recognized by circuit families that contain a constant number of (inner) gates, given a description of the gate types via equations.
['Silke Czarnetzki', 'Andreas Krebs']
I am writing a research paper on a idea Using Duality in Circuit Complexity
[{"from": "human", "value": "I am writing a research paper on a idea Using Duality in Circuit Complexity"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  investigate in a method for proving separation results for abstract classes of languages. A ll established method to characterize varieties of regular languages are identities.  use a recently established generalization of these identities to non-regular languages by Gehrke, Grigorieff, and Pin: so called equations, which are capable of describing arbitrary Boolean algebras of languages. #R##N#While the main concern of their result is the existence of these equations,  investigate in a general method that could allow to find equations for language classes in an inductive manner. #R##N#Thereto  extend an important tool -- the block product or substitution principle -- known from logic and algebra, to non-regular language classes. Furthermore,  abstract this concept by defining it directly as an operation on (non-regular) language classes.  show that this principle can be used to obtain equations for certain circuit classes, given equations for the gate types. #R##N#Concretely,  demonstrate the applicability of this method by obtaining a description via equations for all languages recognized by circuit families that contain a constant number of (inner) gates, given a description of the gate types via equations."}]