Rice's Theorem - Rice's Theorem and Index Sets

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)

    The believing mind reaches its perihelion in the so-called Liberals. They believe in each and every quack who sets up his booth in the fairgrounds, including the Communists. The Communists have some talents too, but they always fall short of believing in the Liberals.
    —H.L. (Henry Lewis)