Private coins versus public coins in interactive proof systems
STOC '86 Proceedings of the eighteenth annual ACM symposium on Theory of computing
Trading group theory for randomness
STOC '85 Proceedings of the seventeenth annual ACM symposium on Theory of computing
Arthur-Merlin games: a randomized proof system, and a hierarchy of complexity class
Journal of Computer and System Sciences - 17th Annual ACM Symposium in the Theory of Computing, May 6-8, 1985
The knowledge complexity of interactive proof systems
SIAM Journal on Computing
Complexity: knots, colourings and counting
Complexity: knots, colourings and counting
The computational complexity of knot and link problems
Journal of the ACM (JACM)
3-manifold knot genus is NP-complete
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Fast algorithms for computing Jones polynomials of certain links
Theoretical Computer Science
Linkless and flat embeddings in 3-space and the unknot problem
Proceedings of the twenty-sixth annual symposium on Computational geometry
The pachner graph and the simplification of 3-sphere triangulations
Proceedings of the twenty-seventh annual symposium on Computational geometry
| Hi-index | 0.00 |
Hass, Lagarias, and Pippenger analyzed the computational complexity of various decision problems in knot theory. They proved that the problem whether a given knot is unknotting is in NP, and conjectured that the problem is contained in NP∩co-NP. Agol, Hass, and Thurston proved that the problem called ManifoldGenus, which is a general problem of Unknotting, is NP-complete. We construct an interactive proof system for Knotting, and prove that the problem is contained in IP(2). Consequently, Unknotting is contained in AM ∩ co-AM. If Unknotting is NP-complete, then Σ2p = Π2p.