Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that the problem of checking careful synchronizability of partial finite automata is PSPACE-complete. Also the problems of checking D 1-, D 2-, and D 3-directability of nondeterministic finite automata are PSPACE-complete; moreover, the restrictions of all these problems to automata with two input letters remain PSPACE-complete.
['Pavel Martyugin']
I am writing a research paper on a idea Computational Complexity of Certain Problems Related to Carefully Synchronizing Words for Partial Automata and Directing Words for Nondeterministic Automata
[{"from": "human", "value": "I am writing a research paper on a idea Computational Complexity of Certain Problems Related to Carefully Synchronizing Words for Partial Automata and Directing Words for Nondeterministic Automata"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  show that the problem of checking careful synchronizability of partial finite automata is PSPACE-complete. Also the problems of checking D 1-, D 2-, and D 3-directability of nondeterministic finite automata are PSPACE-complete; moreover, the restrictions of all these problems to automata with two input letters remain PSPACE-complete."}]