Question 51
A language L is Recursively Enumerable if and only if there exists an Enumerator that -
Language L is RE iff an enumerator exists that eventually prints every string in L.
A language L is Recursively Enumerable if and only if there exists an Enumerator that -
Language L is RE iff an enumerator exists that eventually prints every string in L.
A language L is Recursive (Decidable) if and only if there exists an Enumerator that -
Printing strings in lexicographic order allows determining membership in finite time, proving L is Recursive.
What is the 'Halting Language' $H_{TM}$?
$H_{TM}$ captures the Halting Problem, proving RE complete and undecidable.
What is the 'Empty Language Problem' for Turing Machines $E_{TM}$ = { <M> | L(M) = ∅ }?
$E_{TM}$ testing whether a TM accepts no strings is completely undecidable and non-RE.
What is the 'Equivalence Problem' for Turing Machines EQ_TM = { <M1, M2> | L(M1) = L(M2) }?
Determining language equivalence between two general Turing Machines is non-RE and undecidable.