Unification Algorithms Cannot be Combined in Polynomial Time

@article{Hermann1996UnificationAC,
  title={Unification Algorithms Cannot be Combined in Polynomial Time},
  author={Miki Hermann and Phokion G. Kolaitis},
  journal={Inf. Comput.},
  year={1996},
  volume={162},
  pages={24-42}
}
We establish that there is no polynomial-time general combination algorithm for uniication in nitary equational theories, unless the complexity class #P of counting problems is contained in the class FP of function problems solvable in polynomial-time. The prevalent view in complexity theory is that such a collapse is extremely unlikely for a number of reasons, including the fact that the containment of #P in FP implies that P = NP. Our main result is obtained by establishing the… CONTINUE READING