Abstract
In this chapter we study machines over ℝ that penalize multiplication by modifying their cost in such a way that iterated multiplications become increasingly expensive. This situation is close to the classical where iterated multiplications can generate very large numbers and thus cause an increase in running time. We show that the complexity determined by this modified cost is closely related to the behavior of the algorithm on integer inputs in a very precise sense.
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© 1998 Springer Science+Business Media New York
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Blum, L., Cucker, F., Shub, M., Smale, S. (1998). Weak Machines. In: Complexity and Real Computation. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-0701-6_20
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DOI: https://doi.org/10.1007/978-1-4612-0701-6_20
Publisher Name: Springer, New York, NY
Print ISBN: 978-1-4612-6873-4
Online ISBN: 978-1-4612-0701-6
eBook Packages: Springer Book Archive