Decidability

Question

From http://www.cs.rice.edu/~nakhleh/COMP481/final_review_sp06_sol.pdf

 

$L_{26}=\{<M>|$ M is a TM such that both L(M) and $\lnot L(M)$ are infinite $\}$

I was unable to get proof given in pdf above.Can anyone explain, if someone got it.

Comments

Works almost all the time, let's see if it works in gate !

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Can I take the machine M2 to be the machine that accepts everything?

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it accepts every string of length >= 0, using only $a$