Some consequences of non-uniform conditions on uniform classes.(English)Zbl 0541.68017

Non-uniform complexity classes appear from the circuit complexity. It is proved that if non-uniform classes $$\Sigma_ i/poly=\Pi_ i/poly,$$ then $$\Sigma_{i+2}=\Pi_{i+2}$$ in the Meyer-Stockmeyer hierarchy. Apart that, some connections between coincidence of complexity classes and sparse complete sets are ascertained. If there exists a sparse set which is complete for co-NP relatively to conjunctive reducibility then $$P=NP$$. Besides that, if NP is conjunctively and disjunctively reducible to a sparse NP-complete set then also $$P=NP$$.
Reviewer: D.Yu Grigorev

MSC:

 68Q25 Analysis of algorithms and problem complexity 03D15 Complexity of computation (including implicit computational complexity)
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References:

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