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By Vandenbussche D., Nemhauser G. L.

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Instead of translating the algorithm itself he could preface the program with a complete English course written in French. Another mathematician with a French program and an English machine would follow the opposite procedure. In this way only a fixed number of bits need be added to the program, 36 Thinking about G¨odel & Turing and that number grows less significant as the size of the series specified by the program increases. In practice a device called a compiler often makes it possible to ignore the differences between languages when one is addressing a computer.

ACM, vol. 13, pp. 547–569, October 1966. [12] —, “On the length of programs for computing finite binary sequences: statistical considerations,” J. ACM, vol. 16, pp. 145–159, January 1969. [13] —, “On the simplicity and speed of programs for computing infinite sets of natural numbers,” J. ACM, vol. 16, pp. 407–422, July 1969. [14] P. Martin-L¨ of, “The definition of random sequences,” Inform. and Control, vol. 9, pp. 602–619, December 1966. [15] C. E. Shannon and W. Weaver, The Mathematical Theory of Communication.

From Frege to G¨ odel: A Source Book in Mathematical Logic, 1879–1931. : Harvard Univ. Press, 1967. [2] M. , The Undecidable—Basic Papers on Undecidable Propositions, Unsolvable Problems and Computable Functions. : Raven Press, 1965. [3] J. von Neumann and O. Morgenstern, Theory of Games and Economic Behavior. : Princeton Univ. Press, 1944. 30 Thinking about G¨odel & Turing [4] —, “Method in the physical sciences,” in John von Neumann—Collected Works. New York: Macmillan, 1963, vol. 6, no. 35.

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A branch-and-cut algorithm for nonconvex quadratic programs with box constraints by Vandenbussche D., Nemhauser G. L.

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