# How to prove that a language of machines accepting a fixed string is decideable? [duplicate]

Is L = $\{\langle M,w\rangle \mid \text{$M$accepts string epsilon or string$w$, or both} \}$ decidable?

I attempted to use Rice's Theorem for this question to prove that it is undecidable.

Is my approach in the right direction if I let S, the non-trivial subset of recognizable languages, in this case to be S = {L | $\epsilon$ $\in$ L or $w$ $\in$ L and when both $\in$ L}?

• Have you tried using Rice's theorem to prove this? Apr 19 '18 at 7:27
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– Raphael
Apr 19 '18 at 9:04
• I specified my approach further. Apr 19 '18 at 11:08