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We investigate the problem whether a function of several arguments can bereconstructed from its identification minors. We focus on functions with aunique identification minor, and we establish some positive and negativeresults on the reconstruction problem. In particular, we show that totallysymmetric functions (of sufficiently large arity) are reconstructible and theclass of functions weakly determined by the order of first occurrence (ofsufficiently large arity) is weakly reconstructible.

On the reconstructibility of totally symmetric functions and of other functions with a unique identification minor