theory of computation

Question

This language,

L = { <M,w> / M is a TM,w is a string and M does not halt on string w }

is not recursively enumerable ...right ???

Comments

@Kapil,

 Please explain

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This is the complement of halting problem. Any TOC book should have reason why this is not r.e. If this problem is r.e., then halting problem becomes decidable.

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Thank you.

Answer 1

it is recursive because there is an answer for the string that whether it will halt or not ;

but in recursive enumrable language we know only if it will be acceptable and there is no decidebility for yes or no .