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Explore the complexity of the Minimum Circuit Size Problem (MCSP) and its variants in this IEEE conference talk. Delve into the importance of MCSP, its potential NP-hardness, and its connections to circuit lower bounds. Examine the key ideas behind (Partial Function)-MCSP and (Depth-d Formula)-MCSP. Investigate the power of constant depth formulas and the impact of additional depth. Learn about the proof strategy and the reasoning behind the inductive step in this 23-minute presentation by MIT researcher Rahul Ilango.
Syllabus
Talk Outline
The Minimum Circuit Size Problem (MCSP)
Why care about MCSP?
Is MCSP NP-hard?
MCSP & New Kinds of Circuit Lower Bounds
(Partial Function)-MCSP
Key Ideas
(Depth-d Formula)-MCSP
Constant Depth Formulas
What is the power of extra depth (additively)?
Proof Strategy
Idea behind the inductive step
Taught by
IEEE FOCS: Foundations of Computer Science