Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the circuit complexity of generating at random a word of length n from a given language under uniform distribution.  prove that, for every language accepted in polynomial time by 1-NAuxPDA of polynomially bounded ambiguity, the problem is solvable by a logspace-uniform family of probabilistic boolean circuits of polynomial size and O(log 2  n) depth. Using a suitable notion of reducibility (similar to the NC 1 -reducibility),  also show the relationship beten random generation problems for regular and context-free languages and classical computational complexity classes such as DIV, L and DET.
['Massimiliano Goldwurm', 'Beatrice Palano', 'Massimo Santini']
I am writing a research paper on a idea On the circuit complexity of random generation problems for regular and context-free languages
[{"from": "human", "value": "I am writing a research paper on a idea On the circuit complexity of random generation problems for regular and context-free languages"}, {"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 circuit complexity of generating at random a word of length n from a given language under uniform distribution.  prove that, for every language accepted in polynomial time by 1-NAuxPDA of polynomially bounded ambiguity, the problem is solvable by a logspace-uniform family of probabilistic boolean circuits of polynomial size and O(log 2  n) depth. Using a suitable notion of reducibility (similar to the NC 1 -reducibility),  also show the relationship beten random generation problems for regular and context-free languages and classical computational complexity classes such as DIV, L and DET."}]