Polynomial Time Algorithm Solving the Refutation Tree Problem for Formal Graph Systems

The refutation tree problem is to compute a refutation tree which is associated with the structure of a graph generated by a formal graph system (FGS).We present subclasses of FGSs, called simple FGSs, size-bounded simple FGSs and bounded simple FGSs. In order to show that the refutation tree problem for simple FGSs can be solved in polynomial time, we prove that the refutation tree problem for size-bounded simple FGSs is NC 2 -reducible to the graph ismorphism problem. For bounded simple FGSs, we show that the refutation tree problem is in NC 2 . We present an FGS GI and show that the graph isomorphism problem is log-space reducible to the graph isomorphism problem for