We consider the problem of converting a two-way alternating finite automaton ( 2AFA ) with n states to a 2AFA accepting the complement of its language. Complementing is trivial for halting 2AFA s, by swapping the roles of existential and universal decisions and the roles of accepting and rejecting states. However, since 2AFA s do not have resources to detect infinite loops by counting executed steps, it was not known whether the cost of complementing is polynomial in n in the general case. Here we shall show that 2AFA s can be complemented by using $$O(n^7)$$ O ( n 7 ) states.

中文翻译：

---

双向交替自动机的补码

我们考虑将具有 n 个状态的双向交替有限自动机 (2AFA) 转换为接受其语言补码的 2AFA 的问题。通过交换存在和普遍决策的角色以及接受和拒绝状态的角色，补充对于停止 2AFA 来说是微不足道的。但是，由于 2AFA 没有资源通过计算执行步骤来检测无限循环，因此在一般情况下，不知道补码的成本是否为 n 中的多项式。在这里，我们将证明 2AFA 可以通过使用 $$O(n^7)$$O (n 7 ) 状态来补充。