$$\exists x_{1} \forall x_{2} \ldots \exists x_{n-2} \forall x_{n-1} \exists x_{n} \Phi\left(x_{1}, \ldots, x_{n}\right) ?$$
That is, we wish to know whether there is a choice for $x_{1}$, so that for both choices of $x_{2}$, there is a choice for $x_{3}$, and so on, so that $\Phi$ is satisfied. We will refer to this decision problem as Quantified 3-SAT (or, briefly, QSAT).
The original 3 -SAT problem, by way of comparison, simply asked
$$\exists x_{1} \exists x_{2} \cdots \exists x_{n-2} \exists x_{n-1} \exists x_{n} \Phi\left(x_{1}, \ldots, x_{n}\right) ?$$

In other words, in 3-SAT it was sufficient to look for a single setting of the Boolean variables.

Here’s an example to illustrate the kind of reasoning that underlies an instance of QSAT. Suppose that we have the formula
$$\Phi\left(x_{1}, x_{2}, x_{3}\right)=\left(x_{1} \vee x_{2} \vee x_{3}\right) \wedge\left(x_{1} \vee x_{2} \vee \overline{x_{3}}\right) \wedge\left(\overline{x_{1}} \vee x_{2} \vee x_{3}\right) \wedge\left(\overline{x_{1}} \vee \overline{x_{2}} \vee \overline{x_{3}}\right)$$
$$\exists x_{1} \forall x_{2} \exists x_{3} \Phi\left(x_{1}, x_{2}, x_{3}\right) ?$$

myassignments-help数学代考价格说明

1、客户需提供物理代考的网址，相关账户，以及课程名称，Textbook等相关资料~客服会根据作业数量和持续时间给您定价~使收费透明，让您清楚的知道您的钱花在什么地方。

2、数学代写一般每篇报价约为600—1000rmb，费用根据持续时间、周作业量、成绩要求有所浮动(持续时间越长约便宜、周作业量越多约贵、成绩要求越高越贵)，报价后价格觉得合适，可以先付一周的款，我们帮你试做，满意后再继续，遇到Fail全额退款。

3、myassignments-help公司所有MATH作业代写服务支持付半款，全款，周付款，周付款一方面方便大家查阅自己的分数，一方面也方便大家资金周转，注意:每周固定周一时先预付下周的定金，不付定金不予继续做。物理代写一次性付清打9.5折。

Math作业代写、数学代写常见问题

myassignments-help擅长领域包含但不是全部: