  Characterising tractable fragments of the constraint satisfaction problem
(CSP) is an important challenge in theoretical computer science and artificial
intelligence. Forbidding patterns (generic sub-instances) provides a means of
defining CSP fragments which are neither exclusively language-based nor
exclusively structure-based. It is known that the class of binary CSP instances
in which the broken-triangle pattern (BTP) does not occur, a class which
includes all tree-structured instances, are decided by arc consistency (AC), a
ubiquitous reduction operation in constraint solvers. We provide a
characterisation of simple partially-ordered forbidden patterns which have this
AC-solvability property. It turns out that BTP is just one of five such
AC-solvable patterns. The four other patterns allow us to exhibit new tractable
classes.
