Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Finite automata on infinite words (omega-automata) proved to be a porful apon for modeling and reasoning infinite behaviors of reactive systems. Complementation of omega-automata is crucial#R##N#in many of these applications. But the problem is non-trivial; even after extensive study during the past two decades,  still have an important type of omega-automata, namely Streett automata, for which the gap beten the current best lor bound 2^(Omega(n lg nk)) and upper bound 2^(O (nk lg nk)) is substantial, for the Streett index size k can be exponential in the number of states n. In a previous work  shod a construction for complementing Streett automata with the upper bound 2^(O(n lg n+nk lg k)) for k = O(n) and 2^(O(n^2 lg n)) for k = omega(n).   establish a matching lor bound 2^(Omega (n lg n+nk lg k)) for k = O(n) and 2^(Omega#R##N#(n^2 lg n)) for k = omega(n), and therefore showing that the construction is asymptotically optimal with respect to the ^(Theta(.)) notation.
['Yang Cai', 'Ting Zhang']
I am writing a research paper on a idea A Tight Lower Bound for Streett Complementation
[{"from": "human", "value": "I am writing a research paper on a idea A Tight Lower Bound for Streett Complementation"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: Finite automata on infinite words (omega-automata) proved to be a porful apon for modeling and reasoning infinite behaviors of reactive systems. Complementation of omega-automata is crucial#R##N#in many of these applications. But the problem is non-trivial; even after extensive study during the past two decades,  still have an important type of omega-automata, namely Streett automata, for which the gap beten the current best lor bound 2^(Omega(n lg nk)) and upper bound 2^(O (nk lg nk)) is substantial, for the Streett index size k can be exponential in the number of states n. In a previous work  shod a construction for complementing Streett automata with the upper bound 2^(O(n lg n+nk lg k)) for k = O(n) and 2^(O(n^2 lg n)) for k = omega(n).   establish a matching lor bound 2^(Omega (n lg n+nk lg k)) for k = O(n) and 2^(Omega#R##N#(n^2 lg n)) for k = omega(n), and therefore showing that the construction is asymptotically optimal with respect to the ^(Theta(.)) notation."}]