We prove that it is decidable of a finite algebra whether it has a near-unanimity term operation, which settles a ten-year-old problem. As a consequence, it is decidable of a finite algebra in a congruence distributive variety whether it admits a natural duality.
"The existence of a near-unanimity term in a finite algebra is decidable." J. Symbolic Logic 74 (3) 1001 - 1014, September 2009. https://doi.org/10.2178/jsl/1245158096