On NFAs Where All States are Final, Initial, or Both
  We examine questions involving nondeterministic finite automata where all states are final, initial, or both initial and final. First, we prove hardness results for the nonuniversality and inequivalence problems for these NFAs. Next, we characterize the languages accepted. Finally, we discuss some state complexity problems involving such automata. 
Jui-Yi Kao, Narad Rampersad, and Jeffrey Shallit