On the State Complexity of Operations on Two-Way Finite Automata

• Authors: Galina Jirásková;Alexander Okhotin
• Venue: DLT '08 Proceedings of the 12th international conference on Developments in Language Theory
• Year: 2008

The number of states in two-way deterministic finite automata (2DFAs) is considered. It is shown that the state complexity of basic operations is: at least m+ n茂戮驴 o(m+ n) and at most 4m+ n+ 1 for union; at least m+ n茂戮驴 o(m+ n) and at most m+ n+ 1 for intersection; at least nand at most 4nfor complementation; at least $\Omega(\frac{m}{n}) + \frac{2^{\Omega(n)}}{\log m}$ and at most $2m^{m+1}\cdot 2^{n^{n+1}}$ for concatenation; at least $\frac{1}{n} 2^{\frac{n}{2}-1}$ and at most $2^{O(n^{n+1})}$ for both star and square; between nand n+ 2 for reversal; exactly 2nfor inverse homomorphism. In each case mand ndenote the number of states in 2DFAs for the arguments.