TOC Semi Decidable

Question

Semidecidable means RE or only  but NOT REC? Can i say every semi decidable is undecidable?

Answer 1

Decidable: A problem is a decidable or REC if there exists a TM for this language which can accept the members of the language and reject non-members of the language, both in some finite time. This TM will eventually halt at the end.

Semi-Decidable: A problem is Semi-Decidable or RE, if we have a TM for it which can accept the members of  the language, but for non-members it may or may not halt. It may be a case in which TM is running for infinite time on non-members.

Undecidable Problems: Not RE, No TM exists for such problems neither for members nor for non-members.

You can say every decidable problem is Semi-Decidable too, but can't say a Semi-Decidable is Undecidable problem!!

Comments

Can someone provide an example for a language which is 

1. UD and RE
2. UD and Not RE

@joshi_nitish

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@JEET 

1. UD and RE: Halting problem
2. UD and not RE: Complement of Halting problem 

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Thanks Sir.