We prove that O(e√n log n) states are sufficient to simulate an n-state 1nfa recognizing a unary language by a 1dfa. The lower bound is the same. Similar tight bounds are shown for the simulation of a 2dfa by a 1dfa and a 1nfa. We also show that O(n2) states are sufficient and necessary to simulate an n-state 1nfa recognizing a unary language by a 2dfa. © 1986.
Chrobak, M. (1986). Finite automata and unary languages. Theoretical Computer Science, 47(C), 149–158. https://doi.org/10.1016/0304-3975(86)90142-8