Stronger Lower Bounds for Polynomial Time Problems

08/15/2020

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by   András Z. Salamon, et al.

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We introduce techniques for proving stronger conditional lower bounds for polynomial time problems. In particular, we show that CircuitSat for circuits with m gates and log(m) inputs (denoted by log-CircuitSat) is not decidable in essentially-linear time unless the exponential time hypothesis (ETH) is false and k-Clique is decidable in essentially-linear time in terms of the graph's size for all fixed k. These results offer significant progress towards proving unconditional superlinear time complexity lower bounds for natural problems in polynomial time.