Rice's Theorem and Index Sets
Rice's theorem can be succinctly stated in terms of index sets:
-
Let be a class of partial recursive functions with index set . Then is recursive if and only if or .
where is the set of natural numbers, including zero.
Read more about this topic: Rice's Theorem
Famous quotes containing the words rice, theorem, index and/or sets:
“The arbitrary division of one’s life into weeks and days and hours seemed, on the whole, useless. There was but one day for the men, and that was pay day, and one for the women, and that was rent day. As for the children, every day was theirs, just as it should be in every corner of the world.”
—Alice Caldwell Rice (1870–1942)
“To insure the adoration of a theorem for any length of time, faith is not enough, a police force is needed as well.”
—Albert Camus (1913–1960)
“Exile as a mode of genius no longer exists; in place of Joyce we have the fragments of work appearing in Index on Censorship.”
—Nadine Gordimer (b. 1923)
“Certain anthropologists hold that man, having discovered tools, ceased to evolve biologically. Animals, never having discovered them, continue to fashion drills out of their beaks, oars out of their hind feet, wings out of their forefeet, suits of armor out of their hides, levers out of their horns, saws out of their teeth. Whether this be true or not, all authorities agree that man is the tool-using animal. It sets him off from the rest of the animal kingdom as drastically as does speech.”
—Stuart Chase (1888–1985)