We present a domain-independent algorithm that computes macros in a novel way. Our algorithm computes macros on-the-fly for a given set of states and does not require previously learned or inferred information, nor prior domain knowledge. The algorit
hm is used to define new domain-independent tractable classes of classical planning that are proved to include emph{Blocksworld-arm} and emph{Towers of Hanoi}.
A natural and established way to restrict the constraint satisfaction problem is to fix the relations that can be used to pose constraints; such a family of relations is called a constraint language. In this article, we study arc consistency, a heavi
ly investigated inference method, and three extensions thereof from the perspective of constraint languages. We conduct a comparison of the studied methods on the basis of which constraint languages they solve, and we present new polynomial-time tractability results for singleton arc consistency, the most powerful method studied.
