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ICALP
1995
Springer

New Collapse Consequences of NP Having Small Circuits

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New Collapse Consequences of NP Having Small Circuits
We show that if a self-reducible set has polynomial-size circuits, then it is low for the probabilistic class ZPP(NP). As a consequence we get a deeper collapse of the polynomial-time hierarchy PH to ZPP(NP) under the assumption that NP has polynomial-size circuits. This improves on the well-known result of Karp, Lipton, and Sipser [KL80] stating a collapse of PH to its second level ΣP 2 under the same assumption. As a further consequence, we derive new collapse consequences under the assumption that complexity classes like UP, FewP, and C=P have polynomialsize circuits. Finally, we investigate the circuit-size complexity of several language classes. In particular, we show that for every fixed polynomial s, there is a set in ZPP(NP) which does not have O(s(n))-size circuits.
Johannes Köbler, Osamu Watanabe
Added 26 Aug 2010
Updated 26 Aug 2010
Type Conference
Year 1995
Where ICALP
Authors Johannes Köbler, Osamu Watanabe
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