On a theory of computation over the real numbers' NP completeness, recursive functions and universal machines. Preprint typescript from the library of Martin D. Davis

Blum, Lenore (1942- ); Michael Shub (1943- ); Stephen Smale (1930- ). On a theory of computation over the real numbers NP completeness, recursive functions and universal machines. Offset typescript. 1989. 64pp. 280 x 217 mm. Unbound; stapled. Very good. Rare Preprint Edition. "In computation theory, the BlumShubSmale machine, or BSS machine, is a model of computation introduced by Lenore Blum, Michael Shub and Stephen Smale, intended to describe computations over the real numbers. Essentially, a BSS machine is a Random Access Machine with registers that can store arbitrary real numbers and that can compute rational functions over reals in a single time step. It is closely related to the Real RAM model. "BSS machines are more powerful than Turing machines, because the latter are by definition restricted to a finite set of symbols. A Turing machine can represent a countable set (such as the rational numbers) by strings of symbols, but this does not extend to the uncountable real numbers" (Wikipedia article on Blum-Shub-Smale machine). From the library of Martin Davis. . …