  Singleton arc consistency is an important type of local consistency which has
been recently shown to solve all constraint satisfaction problems (CSPs) over
constraint languages of bounded width. We aim to characterise all classes of
CSPs defined by a forbidden pattern that are solved by singleton arc
consistency and closed under removing constraints. We identify five new
patterns whose absence ensures solvability by singleton arc consistency, four
of which are provably maximal and three of which generalise 2-SAT. Combined
with simple counter-examples for other patterns, we make significant progress
towards a complete classification.
