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Constraint Satisfaction with Countable Homogeneous Templates
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The Complexity of Equality Constraint Languages
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The Complexity of Positive First-order Logic without Equality
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Complexity of Existential Positive First-Order Logic
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Positive first-order logic is NP-complete
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Constraint Satisfaction Problems of Bounded Width
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On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction
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Tractability and Learnability Arising from Algebras with Few Subpowers
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A Tetrachotomy for Positive First-Order Logic without Equality
LICS '11 Proceedings of the 2011 IEEE 26th Annual Symposium on Logic in Computer Science
Quantified Equality Constraints
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The parameterized complexity of maximality and minimality problems
IWPEC'06 Proceedings of the Second international conference on Parameterized and Exact Computation
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We prove a preservation theorem for positive Horn definability in aleph-zero categorical structures. In particular, we define and study a construction which we call the periodic power of a structure, and define a periomorphism of a structure to be a homomorphism from the periodic power of the structure to the structure itself. Our preservation theorem states that, over an aleph-zero categorical structure, a relation is positive Horn definable if and only if it is preserved by all periomorphisms of the structure. We give applications of this theorem, including a new proof of the known complexity classification of quantified constraint satisfaction on equality templates.