Rice's Theorem
If A is a class of recursively enumerable sets, then the set of Gödel numbers of functions whose domains belong to A is called its index set. If the index set of A is a recursive set, then either A is empty or A contains all recursively enumerable sets.
Rice's theorem is an important result for computer science because it sets up boundaries for research in that area. It basically states that only trivial properties of programs are algorithmically decidable.
See also
Decidable, Gödel Number, Recursively Enumerable Set, UndecidableThis entry contributed by Alex Sakharov (author's link)
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References
Davis, M. Computability and Unsolvability. New York: Dover, 1982.Rice, H. G. "Classes of Recursively Enumerable Sets and Their Decision Problems." Trans. Amer. Math. Soc. 74, 358-366, 1953.Rogers, H. Theory of Recursive Functions and Effective Computability. Cambridge, MA: MIT Press, 1987.Wolfram, S. A New Kind of Science. Champaign, IL: Wolfram Media, p. 1137, 2002.Referenced on Wolfram|Alpha
Rice's TheoremCite this as:
Sakharov, Alex. "Rice's Theorem." From MathWorld--A Wolfram Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/RicesTheorem.html