NP-completeness Results for NONOGRAM via Parsimonious Reductions

We introduce a new class of NP problems called ANOTHER SOLUTION PROBLEMs.For a given NP problem X, ANOTHER SOLUTION PROBLEM for X (ASP for X) is toask, for a given instance I for X and its solution, whether there is another solution for I.The diculty of ASP for X may not be immediate from the diculty of X. For example,for some NP-complete problems such as 3SAT or 3DM, it is easy to show that their ASPsare NP-complete; on the other hand, ASP for, e.g., VERTEX COLORING is trivially in P....