A faster solver for general systems of equations

We present a new algorithm which computes a partial approximate solution for a system of equations. It is local in that it considers just as many variables as necessary in order to compute the values of those variables we are interested in, it is generic in that it makes no assumptions on the application domain, and it is general in that the algorithm does not depend on any specific properties of right-hand sides of equations. For instance, monotonicity is not required. However, in case the right-hand sides satisfy some weak monotonicity property, our algorithm returns the (uniquely defined) least solution. The algorithm meets the best theoretical worstcase complexity known for similar algorithms. For the application of analyzing logic languages, it also gives the best practical results on most of our real-world benchmark programs.