The Undecidable Problem in Computability Theory
In computability theory, the halting problem is a decision problem which can be stated as follows:
- Given the description of an arbitrary program and a finite input, decide whether the program finishes running or will run forever.
Alan Turing proved in 1936 that a general algorithm running on a Turing machine that solves the halting problem for all possible program-input pairs necessarily cannot exist. Hence, the halting problem is undecidable for Turing machines.
Read more about this topic: Undecidable Problem
Famous quotes containing the words problem and/or theory:
“Like the effects of industrial pollution ... the AIDS crisis is evidence of a world in which nothing important is regional, local, limited; in which everything that can circulate does, and every problem is, or is destined to become, worldwide.”
—Susan Sontag (b. 1933)
“Every theory is a self-fulfilling prophecy that orders experience into the framework it provides.”
—Ruth Hubbard (b. 1924)