Satisfiability Algorithms for Restricted Circuit Classes

In recent years, finding new satisfiability algorithms for various circuit classes has been a very active line of research. Despite considerable progress, we are still far away from a definite answer on which circuit classes allow fast satisfiability algorithms. This survey takes a (far from exhaustive) look at some recent satisfiability algorithms for a range of circuit classes and highlights common themes. A special focus is given to connections between satisfiability algorithms and circuit lower bounds. A second focus is on reductions from satisfiability algorithms to a range of polynomial time problems, such as matrix multiplication and the Vector Domination Problem.