Arkadev Chattopadhyay, Jacobo Toran, Fabian Wagner

We give a new upper bound for the Group and Quasigroup

Isomorphism problems when the input structures

are given explicitly by multiplication tables. We show that these problems can be computed by polynomial size nondeterministic circuits of unbounded fan-in with $O(\log\log n)$ depth and $O(\log^2 n)$ nondeterministic bits, ...
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Eric Allender, Joshua Grochow, Dieter van Melkebeek, Cris Moore, Andrew Morgan

We study the computational power of deciding whether a given truth-table can be described by a circuit of a given size (the Minimum Circuit Size Problem, or MCSP for short), and of the variant denoted as MKTP where circuit size is replaced by a polynomially-related Kolmogorov measure. All prior reductions ... more >>>