 
Summary: The Isomorphism Conjecture
Manindra Agrawal
IIT Kanpur
CiE, Heidelberg, July 22, 2009
Manindra Agrawal (IITK) The Isomorphism Conjecture CiE 2009 1 / 49
Outline
1 Formulation
2 Proving the Conjecture
3 A Counter Conjecture
4 Isomorphism Conjecture in Other Settings
For Classes other than NP
For Degrees other than Complete Degree
For Reducibilities other than Polynomialtime
5 Back to the Isomorphism Conjecture
Manindra Agrawal (IITK) The Isomorphism Conjecture CiE 2009 2 / 49
The Isomorphism Theorem for c.e. Class
Theorem (Myhill, 1955)
Let A and B be two mcomplete sets for c.e.. Then A B.
mcomplete : manyone complete
: isomorphic under computable isomorphisms
