Norman Shapiro
American mathematician
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Mathematics
Norman Shapiro's Degrees
- PhD Mathematics University of California, Berkeley
- Bachelors Mathematics University of California, Berkeley
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Why Is Norman Shapiro Influential?
(Suggest an Edit or Addition)According to Wikipedia, Norman Zalmon Shapiro was an American mathematician, who was the co-author of the Rice–Shapiro theorem. Education Shapiro obtained a BS in Mathematics at University of Illinois in 1952. Shapiro spent the summer of 1954 at Bell Laboratories in Murray Hill, New Jersey where, in collaboration with Karel de Leeuw, Ed Moore, and Claude Shannon, he investigated the question of whether providing a Turing machine augmented with an oracle machine producing an infinite sequence of random events would enable the machine to output a non-computable sequence. The well-known efficacy of Monte Carlo methods might have led one to think otherwise, but the result was negative. Stated precisely:An infinite string, S, on a finite alphabet is computable if it can be output with probability one by a Turing machine augmented by an oracle machine giving an infinite sequence of equal-probability zeroes and ones.Moreover, the result continues to hold if the output probability is any positive number, and the probability of an oracle machine inquiry yielding 1 is any computable real number.
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