text: A value named for this scenario is defined as the sum over all inputs p of "two raised to the negative of the absolute value of the length of p" and is an example of a Martin-Lof random sequence.
full_question: A value named for this scenario is defined as the sum over all inputs p of "two raised to the negative of the absolute value of the length of p" and is an example of a Martin-Lof random sequence. The proof of the principal theorem resulting from this scenario relies on constructing a model whose two inputs are another model of the same type as well a string, then having that first model output the opposite of the second model; afterwards it is shown that there is a contradiction if both models are the same. A reduction of this scenario is used to prove that computing a non-trivial partial function is impossible, a result known as Rice's theorem. Chaitin's constant gives the probability that a program successfully resolves this scenario. The insolvability of the Post correspondence problem relies on reducing it to this other problem. For 10 points, name this undecidable decision problem which asks if a Turing Machine will stop for a given input.
first_sentence: A value named for this scenario is defined as the sum over all inputs p of "two raised to the negative of the absolute value of the length of p" and is an example of a Martin-Lof random sequence.
raw_answer: halting problem