  In this paper we investigate the computational complexity of deciding if a
given finite algebraic structure satisfies a fixed (strong) Maltsev condition
$\Sigma$. Our goal in this paper is to show that $\Sigma$-testing can be
accomplished in polynomial time when the algebras tested are idempotent and the
Maltsev condition $\Sigma$ can be described using paths. Examples of such path
conditions are having a Maltsev term, having a majority operation, and having a
chain of J\'onsson (or Gumm) terms of fixed length.
