We prove that if a finite algebra $\m a$ generates a congruence distributive variety, then the subalgebras of the powers of $\m a$ satisfy a certain kind of intersection property that fails for finite idempotent algebras that locally exhibit affine or unary behaviour. We demonstrate a connection between this property and the constraint satisfaction problem.

Keywords:

congruence distributive, constraint satisfaction problem, tame congruence theory, \jon terms, Mal'cev condition congruence distributive, constraint satisfaction problem, tame congruence theory, \jon terms, Mal'cev condition

MSC Classifications:

08B10, 68Q25, 08B05 show english descriptions Congruence modularity, congruence distributivity
Analysis of algorithms and problem complexity [See also 68W40]
Equational logic, Mal'cev (Mal'tsev) conditions 08B10 - Congruence modularity, congruence distributivity
68Q25 - Analysis of algorithms and problem complexity [See also 68W40]
08B05 - Equational logic, Mal'cev (Mal'tsev) conditions

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