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- W4300769385 abstract "We study techniques for deciding the computational complexity of infinite-domain constraint satisfaction problems. For certain fundamental algebraic structures Delta, we prove definability dichotomy theorems of the following form: for every first-order expansion Gamma of Delta, either Gamma has a quantifier-free Horn definition in Delta, or there is an element d of Gamma such that all non-empty relations in Gamma contain a tuple of the form (d,...,d), or all relations with a first-order definition in Delta have a primitive positive definition in Gamma. The results imply that several families of constraint satisfaction problems exhibit a complexity dichotomy: the problems are in P or NP-hard, depending on the choice of the allowed relations. As concrete examples, we investigate fundamental algebraic constraint satisfaction problems. The first class consists of all first-order expansions of (Q;+). The second class is the affine variant of the first class. In both cases, we obtain full dichotomies by utilising our general methods." @default.
- W4300769385 created "2022-10-04" @default.
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- W4300769385 date "2010-05-07" @default.
- W4300769385 modified "2023-09-27" @default.
- W4300769385 title "Horn versus full first-order: complexity dichotomies in algebraic constraint satisfaction" @default.
- W4300769385 doi "https://doi.org/10.48550/arxiv.1005.1141" @default.
- W4300769385 hasPublicationYear "2010" @default.
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