All reports by Author Cody Murray:

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TR19-075
| 25th May 2019
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Lijie Chen, Dylan McKay, Cody Murray, Ryan Williams#### Relations and Equivalences Between Circuit Lower Bounds and Karp-Lipton Theorems

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TR17-188
| 22nd December 2017
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Cody Murray, Ryan Williams#### Circuit Lower Bounds for Nondeterministic Quasi-Polytime: An Easy Witness Lemma for NP and NQP

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TR14-164
| 30th November 2014
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Cody Murray, Ryan Williams#### On the (Non) NP-Hardness of Computing Circuit Complexity

Lijie Chen, Dylan McKay, Cody Murray, Ryan Williams

Relations and Equivalences Between Circuit Lower Bounds and Karp-Lipton Theorems

A frontier open problem in circuit complexity is to prove P^NP is not in SIZE[n^k] for all k; this is a necessary intermediate step towards NP is not in P/poly. Previously, for several classes containing P^NP, including NP^NP, ZPP^NP, and ... more >>>

Cody Murray, Ryan Williams

We prove that if every problem in $NP$ has $n^k$-size circuits for a fixed constant $k$, then for every $NP$-verifier and every yes-instance $x$ of length $n$ for that verifier, the verifier's search space has an $n^{O(k^3)}$-size witness circuit: a witness for $x$ that can be encoded with a circuit ... more >>>

Cody Murray, Ryan Williams

The Minimum Circuit Size Problem (MCSP) is: given the truth table of a Boolean function $f$ and a size parameter $k$, is the circuit complexity of $f$ at most $k$? This is the definitive problem of circuit synthesis, and it has been studied since the 1950s. Unlike many problems of ... more >>>