Abstract
Two recursive sets A and B form a minimal pair with respect to some polynomial time reducibility notion ≤pr if neither A nor B can be computed in polynomial time but every set which reduces to both A and B is polynomial time computable. We show that for every recursive set A∉P there is a recursive set B such that A and B form a minimal pair. Moreover, similar results for pairs without greatest predecessors are proved.
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© 1987 Springer-Verlag Berlin Heidelberg
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Ambos-Spies, K. (1987). Minimal pairs for polynomial time reducibilities. In: Börger, E. (eds) Computation Theory and Logic. Lecture Notes in Computer Science, vol 270. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18170-9_149
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DOI: https://doi.org/10.1007/3-540-18170-9_149
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