We study the complexity of infinite-domain constraint satisfaction problems:
our basic setting is that a complexity classification for the CSPs of
first-order expansions of a structure A can be transferred to a
classification of the CSPs of first-order expansions of another structure
B. We exploit a product of structures (the algebraic product) that
corresponds to the product of the respective polymorphism clones and present a
complete complexity classification of the CSPs for first-order expansions of
the n-fold algebraic power of (Q;<). This is proved by various
algebraic and logical methods in combination with knowledge of the
polymorphisms of the tractable first-order expansions of (Q;<) and
explicit descriptions of the expressible relations in terms of syntactically
restricted first-order formulas. By combining our classification result with
general classification transfer techniques, we obtain surprisingly strong new
classification results for highly relevant formalisms such as Allen's Interval
Algebra, the n-dimensional Block Algebra, and the Cardinal Direction
Calculus, even if higher-arity relations are allowed. Our results confirm the
infinite-domain tractability conjecture for classes of structures that have
been difficult to analyse with older methods. For the special case of
structures with binary signatures, the results can be substantially
strengthened and tightly connected to Ord-Horn formulas; this solves several
longstanding open problems from the AI literature.Comment: 61 pages, 1 figur