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Ultimate Polynomial Time

By Gregorio Malajovich


The class UP of ‘ultimate polynomial time ’ problems over C is introduced; it contains the class P of polynomial time problems over C. The τ-Conjecture for polynomials implies that UP does not contain the class of non-deterministic polynomial time problems definable without constants over C. This latest statement implies that P ̸ = N P over C. A notion of ‘ultimate complexity ’ of a problem is suggested. It provides lower bounds for the complexity of structured problems.

Year: 1999
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