Suppose i want to program a 3-SAT solver. I want my solver to first check whether a formula is in the list of 3-CNF that currently known can be solved in polynomial time before resorting to brute force.
Wikipedia page https://en.wikipedia.org/wiki/Boolean_satisfiability_problem listed the following formula as solvable in polynomial time: 2-CNF, XOR Formula, Horn Formula, Renamable Horn Formula, Dual Horn Formula, Renamable Dual Horn Formula.
Have anyone found polynomial time algorithm to find whether a formula is Renamable XOR formula ? Is there any other form of 3-CNF formula that can be solved in polynomial time but is not listed above