  It is a conjecture that the signature of a positive link is bounded below by
an increasing function of its negated Euler characteristic. In relation to this
conjecture, we apply the generator description for canonical genus to show that
the boundedness of the genera of positive knots with given signature can be
algorithmically partially decided. We relate this to the result that the set of
knots of canonical genus greater than or equal to n is dominated by a finite
subset of itself in the sense of Taniyama's partial order.
