Computationally Related Problems

We look at several problems from areas such as network flows, game theory, artificial intelligence, graph theory, integer programming and nonlinear programming and show that they are related in that any one of these problems is solvable in polynomial time if all the others are, too. At present, no polynomial time algorithm for these problems is known. These problems extend the equivalence class of problems known as P-Complete. The problem of deciding whether the class of languages accepted by polynomial time nondeterministic Turing machines is the same as that accepted by polynomial time deterministic Turing machines is related to P-Complete problems in that these two classes of languages are the same if each P-Complete problem has a polynomial deterministic solution. In view of this, it appears very likely that this equivalence class defines a class of problems that cannot be solved in deterministic polynomial time.