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Halo2 uses the lookup argument technique, allowing to run lookup on any random sets. It is of more universality than the Plookup technique because the latter requires the same types of elements while the sizes can be different.
Firstly we go through technique description, without zero knowledge in which we will express "lookup" by discussing the "subset argument" between two sets of data on one table. Then we introduce zero knowledge and at the end we see some generalized conditions for which above lookup argument can be used.