Richardson,s Theorem
المؤلف:
Caviness, B. F
المصدر:
"On Canonical Forms and Simplification." J. Assoc. Comp. Mach. 17
الجزء والصفحة:
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20-1-2022
2461
Richardson's Theorem
Let 
be the class of expressions generated by
1. The rational numbers and the two real numbers 
and 
,
2. The variable 
,
3. The operations of addition, multiplication, and composition, and
4. The sine, exponential, and absolute value functions.
Then if 
, the predicate "
" is recursively undecidable.
REFERENCES
Caviness, B. F. "On Canonical Forms and Simplification." J. Assoc. Comp. Mach. 17, 385-396, 1970.
Davenport, J. H. J. Symb. Comput. 34, 259, 2002.
Petkovšek, M.; Wilf, H. S.; and Zeilberger, D. A=B. Wellesley, MA: A K Peters, 1996.
http://www.cis.upenn.edu/~wilf/AeqB.html.Richardson, D. "Some Unsolvable Problems Involving Elementary Functions of a Real Variable." J. Symbolic Logic 33, 514-520, 1968.Richardson, D. J. Symb. Comput. 24, 627, 1997.
Richardson, D. In Computability and Complexity in Analysis (Ed. J. Blanck, V. Brattka, and P. Hertling). Berlin: Springer-Verlag, 2000.
Trott, M. The Mathematica GuideBook for Symbolics. New York: Springer-Verlag, 2005. http://www.mathematicaguidebooks.org/.
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