New tractable classes from old

The constraint satisfaction problem is known to be NP-hard in general, but a number of restrictions of the problem have been identified over the years which ensure tractability. This paper introduces two simple methods of combining two or more tractable classes over disjoint domains, in order to synthesise larger, more expressive tractable classes. We demonstrate that the classes so obtained are genuinely novel, and have not been previously identified. In addition, we use algebraic techniques to extend the tractable classes which we identify, and to show that the algorithms for solving these extended classes can be less than obvious.