Would polynomial solution for #P-complete problem mean polynomial solution for PSPACE problem? After looking at textbooks and trying to derive by my own deductive abilities, I was not able to see whether polynomial solution for #P-complete problem (that is counting problem done in polynomial time) do or do not lead to polynomial solution for PSPACE problem. Can anyone show me why it has to be one or the other way?
We know that #P is included in FPSPACE (the class of function problems corresponding to PSPACE), but we currently do not know if this inclusion is proper or not. Therefore, a polynomial time algorithm for #P-complete problems does not necessarily imply a polynomial time algorithm for all problems in PSPACE.