Rice,s Theorem
المؤلف:
Davis, M
المصدر:
Computability and Unsolvability. New York: Dover, 1982.
الجزء والصفحة:
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20-1-2022
1324
Rice's Theorem
If 
is a class of recursively enumerable sets, then the set of Gödel numbers of functions whose domains belong to 
is called its index set. If the index set of 
is a recursive set, then either 
is empty or 
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.
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.
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