  We give a complete characterization of polynomials in two complex variables
that are cyclic with respect to the coordinate shifts acting on Dirichlet-type
spaces in the bidisk, which include the Hardy space and the Dirichlet space of
the bidisk. The cyclicity of a polynomial depends on both the size and nature
of the zero set of the polynomial on the distinguished boundary. The techniques
in the proof come from real analytic function theory, determinantal
representations for stable polynomials, and harmonic analysis on curves
