Description

1. Let A be a Turing-recognizable language consisting of Turing machines, {hM1i,hM2i,…}, where every Mi is a decider. Prove that some decidable language D is not decided by any decider Mi whose description appears in A.
2. Let A = {hRi| R is a regular expression describing a language containing at least one string w that has 111 as a substring (i.e. w = x111y for some x and y }. Show that A is decidable.
3. Let A = {hR,Si| R and S are regular expressions and L(R) ⊆ L(S)}. Show that A is decidable.
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