Mittagsseminar (in cooperation with J. Lengler, A. Steger, and D. Steurer)

Date and Time: Tuesday, October 24, 2017, 12:15 pm

Duration: 30 minutes

Location: OAT S15/S16/S17

Speaker: Thomas Dueholm Hansen (Aarhus University)

Simulating Branching Programs with Edit Distance and Friends or: A Polylog Shaved is a Lower Bound Made

Backurs and Indyk (STOC'15) recently proved that the Edit Distance of two sequences of equal length cannot be computed in strongly subquadratic time under the Strong Exponential Time Hypothesis (SETH). The result was extended by follow-up works to similar problems such as finding the Longest Common Subsequence (LCS).

SETH is a very strong assumption: it asserts that even linear size CNF formulas cannot be analyzed for satisfiability with an exponential speedup over exhaustive search. We consider much safer assumptions, e.g. that such a speedup is impossible for SAT on much more expressive representations, like subexponential-size NC circuits.

Our main result is a reduction from SAT on Branching Programs to fundamental problems like Edit Distance and LCS. Truly subquadratic algorithms for these problems therefore have consequences that we consider to be far more remarkable than merely faster CNF SAT algorithms. An interesting feature of our work is that even mildly subquadratic algorithms imply new circuit lower bounds. For example, we show that if we can shave an arbitrarily large polylog factor from the complexity of Edit Distance then NEXP does not have non-uniform NC^1 circuits.

Joint work with Amir Abboud, Virginia Vassilevska Williams, and Ryan Williams.

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