Abstract
Polynomial completeness results aim at characterizing those functions that are induced by polynomials. Each polynomial function is congruence preserving, but the opposite need not be true. A finite algebraic structure [Formula: see text] is called strictly 1-affine complete if every unary partial function from a subset of [Formula: see text] to [Formula: see text] that preserves the congruences of [Formula: see text] can be interpolated by a polynomial function of [Formula: see text]. The problem of characterizing strictly 1-affine complete finite Mal’cev algebras is still open. In this paper, we extend the characterization by Aichinger and Idziak of strictly 1-affine complete expanded groups to finite congruence regular Mal’cev algebras.
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