I have been doing some research in Gauss codes and have been reading Kauffman's paper Virtual Knot Theory. In section 3.3, Theorem 2, he states that
If $K$ is a virtual knot whose underlying Gauss code is planar and whose sign sequence is standard, then $K$ is equivalent to a classical knot.
He then goes on to say that "The fundamental problem in Gauss codes is to give an algorithm for determining whether a given code can be realized by a planar shadow."
One problem I have is that I can't figure out what exactly the word standard means in the theorem - he says he will define it later and never does. And does he actually solve this "fundamental problem" in the rest of the section 3.3. If anyone knows a technical definition of standard, I would be very appreciative.
The point is to figure out if the the follow question is open:
Given a Gauss Code, is there an (explicit) algorithm for detecting if it can be realized as a classical knot?
So if you know that it is or is not open, I would love to know too. In the case that it is known, a reference would be wonderful too. Thanks.