# Common method for solving satisfiability problems which lie in P

I know from Schaefer's Dichotomy Theorem that only a few types of satisfiability problems are in P and any other problem is NP-complete. However, all of the algorithms I know for them use specific techniques unique to that type of problem- e.g. unit propagation for Hornsat, linear algebraic techniques mod 2 for XORSAT, and various other techniques for 2-sat. Is there one general polytime algorithm which works for all of these problems in P? Thanks.

• the question is not actually all that meaningful because there is no technical way to differentiate "different algorithms". an algorithm that calls lots of different algorithms as subroutines is still an algorithm. however, there is a natural conjecture here that maybe a more unified approach exists. – vzn Jan 27 '15 at 18:31

• Given a formula $f$, are there algorithms to determine which category $f$ falls into? – hengxin Jan 29 '15 at 5:54