Intermediate
Theory of Computation
Q63 / 100
What is the relationship between decidability and semi-decidability?
Correct! Well done.
Incorrect.
The correct answer is B) Decidable implies semi-decidable (recognizable). A problem is decidable iff it and its complement are both semi-decidable
B
Correct Answer
Decidable implies semi-decidable (recognizable). A problem is decidable iff it and its complement are both semi-decidable
Explanation
If L and L̄ are both RE, then L is decidable. For a recognizer of L: run it and a recognizer of L̄ in parallel; whichever halts first decides. This is Turing's decidability characterization.
Progress
63/100