Complement for Two-Way Alternating Automata

We consider the problem of converting a two-way alternating finite automaton (2AFA) with n states to a 2AFA accepting the complement of the original language. Complementing is trivial for halting 2AFAs, by inverting the roles of existential and universal decisions and the roles of accepting and rejecting states. However, since 2AFAs do not have resources to detect infinite loops by counting executed steps, the best construction known so far required Omega(4(n)) states. Here we shall show that the cost of complementing is polynomial in n. This complementary simulation does not eliminate infinite loops.