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:
“... there has been a very special man in my life for the past year. All I’ll say about him is that he’s kind, warm, mature, someone I can trust—and he’s not a politician.”
—Donna Rice (b. c. 1962)
“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)
“Drink, sir, is a great provoker of three things ... nose-painting, sleep, and urine. Lechery, sir, it provokes and unprovokes: it provokes the desire but it takes away the performance. Therefore much drink may be said to be an equivocator with lechery: it makes him and it mars him; it sets him on and it takes him off.”
—William Shakespeare (1564–1616)