Abstract
Picture a very large bundle of knotted string. How many twists might it take to untie it into a straight lace? Although simple in concept, the problem of determining whether a knot can be untangled within a bounded number of moves, and whether it represents another knot, belongs to NP ∩ co-NP, but no polynomial-time algorithm is known. Existing tools for exploring knots primarily focus on identifying them through invariants and visualizations, making transformations manual and difficult to execute computationally. This paper explores the components necessary to reframe the problem through a novel data structure called the Easy Knot. This structure is designed to parametrize knots in a way that enables automated generation, untangling, and comparison, thereby providing a new perspective on the computational complexity of knot simplification and equivalence.