Undecidable problems

problem of determining whether a given program will finish running or continue forever

In mathematics and computer science, the ; ) is a challenge posed by David Hilbert and Wilhelm Ackermann in 1928. It asks for an algorithm that considers an inputted statement and answers "yes" or "no" according to whether it is universally valid, i.e., valid in every structure. Such an algorithm was proven to be impossible by Alonzo Church and Alan Turing in 1936.

undecidable decision problem

theorem in computability theory

decision problem for which it is impossible to construct an algorithm that always leads to a correct yes-or-no answer

Mathematics problem

class of formal systems modelled visually by equal-sized squares with a color on each edge which can be arranged side by side

complexity class

class of all decision problems

given a finitely generated group, the algorithmic problem of deciding whether two words in the generators represent the same element