On the state complexity of operations on two-way finite automata

Abstract

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-o(m+n) and at most 4m+n+1 for union; at least m+n-o(m+n) and at most m+n+1 for intersection; at least n and at most 4n for complementation; at least Ω(m/n)+2ω(n)/log m and at most 2mm+1 . 2n n+1for concatenation; at least 1/n 2 n/2-1and at most 2O(n n+1)for both star and square; between n and n+2 for reversal; exactly 2n for inverse homomorphism. In each case m and n denote the number of states in 2DFAs for the arguments. © 2008 Springer-Verlag Berlin Heidelberg.