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Question: enter image description here

My answer is no, because it loops forever. But I am a bit unsure if this is the right answer.

Thomas Andrews
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TheFermat
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  • What is "it" when you say "it loops forever?" What do you think "Turing-recognizable" means? What do you think the definition of $B$ means? – Thomas Andrews Jan 31 '16 at 14:07
  • $B$ is a set of strings -- specifically the set that contains ${abc, aabbcc, aaabbbccc, \dots}$. So the question that's being asked above is: can you program a Turing machine so that it accepts these and only these strings? – Eli Rose Jan 31 '16 at 14:18
  • What loops forever? Only a specific TM can do that. You claim that any TM recognizing $B$ must do so? Then how would it recognize $B$? Makes no sense. – BrianO Jan 31 '16 at 15:25

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Construct a Turing machine that checks it is $a$s followed by $b$s and by $c$s, if not, reject. Go back to the beginning, cross out an $a$, a $b$ and a $c$, and start over at the beginning. If no uncrossed symbols remain, accept.

As it is accepted by the Turing machine outlined, the language is Turing recognizable.

vonbrand
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