定理5.3是关于Regular_TM = {M |的可判定性M是图灵机(TM),L(M)是常规语言}。为了达到矛盾,TM R被假定为Regular_TM的决策者,然后R用于决定接受问题,如打击TM S所示:
S = "On input (M,w) where M is a TM and w is a string:
1. Construct the code of TM M2 as follows:
M2 = "On input x:
(a) If x of the form 0^n1^n, accept.
(b) else, run M on w and if M accepts w, then accept."
2. Run R on (M2).
3. If R accepts, accept; if R rejects, reject."
我有两个问题。第一个是M_2固定的?如果没有,它来自哪里?
第二个问题。为什么我们关心M2中的x。如果R确实是一个决策者,我们为什么要关心检查x是否在0 ^ n1 ^ n。下面的TM S'也适用吗?
S = "On input (M,w) where M is a TM and w is a string:
1. Construct the code of TM M2 as follows:
M2 = "On input x: //ignore x
(a) run M on w and if M accepts w, then accept else reject."
2. Run R on (M2).
3. If R accepts, accept; if R rejects, reject."