  We define and study a bigraded knot invariant whose Euler characteristic is
the Alexander polynomial, closely connected to knot Floer homology. The
invariant is the homology of a chain complex whose generators correspond to
Kauffman states for a knot diagram. The definition uses decompositions of knot
diagrams: to a collection of points on the line, we associate a differential
graded algebra; to a partial knot diagram, we associate modules over the
algebra. The knot invariant is obtained from these modules by an appropriate
tensor product.
