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Amplifying lower bounds by means of self-reducibility
2010
Journal of the ACM
We observe that many important computational problems in NC 1 share a simple self-reducibility property. We then show that, for any problem A having this self-reducibility property, A has polynomial size TC 0 circuits if and only if it has TC 0 circuits of size n 1+ for every > 0 (counting the number of wires in a circuit as the size of the circuit). As an example of what this observation yields, consider the Boolean Formula Evaluation problem (BFE), which is complete for NC 1 . It follows from
doi:10.1145/1706591.1706594
fatcat:on7yqocrijckhbbamxiui3aolu