Resource bounded immunity and simplicity
Theoretical Computer Science
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Kolmogorov complexity has proven to be a very useful tool in simplifying and improving proofs that use complicated combinatorial arguments. Using Kolmogorov complexity for oracle construction, we obtain separation results that are much stronger than separations obtained previously even with the use of very complicated combinatorial arguments. Moreover the use of Kolmogorov arguments almost trivializes the construction itself.In particular we construct relativized worlds where: -The intersection of NP and CoNP has a set that is not in P/poly. -NP has a set that is both simple and immune for the intersection of NP and CoNP. -CoNP has a set that is both simple and immune for the intersection of NP and CoNP. -Pi_2, one of the classes in the second level of the Polynomial Hierarchy, has a set that is both simple and immune for the intersection of Pi_2 and Sigma_2.