Question

the halting problem is undecidable. this implies that there exists an input w for every program p such that it is undecidable if p will halt on w. true false

Answer 1

True. The halting problem is undecidable, meaning there exists an input for every program that is undecidable whether it will halt.

Step-by-step explanation:

Yes, it is true that the halting problem is undecidable. This means that there exists an input w for every program p such that it is undecidable whether p will halt on w.

This concept was first proven by Alan Turing in 1936. He showed that there is no algorithm that can determine, for any arbitrary program and input, whether the program will eventually halt or run indefinitely.

This result has significant implications in computer science and has applications in various areas such as software verification and program analysis.