  We describe rules for computing a homology theory of knots and links in
$\mathbb{R}^3$. It is derived from the theory of framed BPS states bound to
domain walls separating two-dimensional Landau-Ginzburg models with (2,2)
supersymmetry. We illustrate the rules with some sample computations, obtaining
results consistent with Khovanov homology. We show that of the two
Landau-Ginzburg models discussed in this context by Gaiotto and Witten one,
(the so-called Yang-Yang-Landau-Ginzburg model) does not lead to topological
invariants of links while the other, based on a model with target space equal
to the universal cover of the moduli space of $SU(2)$ magnetic monopoles, will
indeed produce a topologically invariant theory of knots and links.
