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)
“To me this world is all one continued vision of fancy or imagination, and I feel flattered when I am told so. What is it sets Homer, Virgil and Milton in so high a rank of art? Why is Bible more entertaining and instructive than any other book? Is it not because they are addressed to the imagination, which is spiritual sensation, and but mediately to the understanding or reason?”
—William Blake (1757–1827)