The Minimum Circuit Size Problem (MCSP) asks to determine the minimum size of a circuit computing a given truth table. MCSP is a natural and powerful string compression problem whose NPhardness remains open. Recently, Oliveira and Santhanam [FOCS 2018] and Oliveira, Pich, and Santhanam [ECCC 2018] demonstrated a "hardness magnification" phenomenon for MCSP in restricted settings. Letting MCSP[s(n)] be the problem of deciding if a truth table of length 2 n has circuit complexity at most s(n), they proved that small (fixed-polynomial) average case circuit/formula lower bounds for MCSP[2 √ n ], or lower bounds for approximating * Supported by NSF CAREER 1741615. † Portions of this work were completed while the author was a PhD student at MIT, and as a Research Fellow at the Simons Institute, UC Berkeley.

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