Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: It is ll known that the resulting language obtained by inserting a regular language to a regular language is regular.  study the nondeterministic and deterministic state complexity of the insertion operation. Given two incomplete DFAs of sizes m and n,  give an upper bound (m+2)·2mn−m−1·3m and find a lor bound for an asymp-totically tight bound.  also present the tight nondeterministic state complexity by a fooling set technique. The deterministic state complexity of insertion is 2Θ(mn) and the nondeterministic state complexity of insertion is precisely mn+2m, where m and n are the size of input finite automata.  also consider the state complexity of insertion in the case where the inserted language is bifix-free or non-returning.
['Yo-Sub Han', 'Sang-Ki Ko', 'Timothy Ng', 'Kai Salomaa']
I am writing a research paper on a idea State Complexity of Insertion
[{"from": "human", "value": "I am writing a research paper on a idea State Complexity of Insertion"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely: It is ll known that the resulting language obtained by inserting a regular language to a regular language is regular.  study the nondeterministic and deterministic state complexity of the insertion operation. Given two incomplete DFAs of sizes m and n,  give an upper bound (m+2)\u00b72mn\u2212m\u22121\u00b73m and find a lor bound for an asymp-totically tight bound.  also present the tight nondeterministic state complexity by a fooling set technique. The deterministic state complexity of insertion is 2\u0398(mn) and the nondeterministic state complexity of insertion is precisely mn+2m, where m and n are the size of input finite automata.  also consider the state complexity of insertion in the case where the inserted language is bifix-free or non-returning."}]