Majority functions on structures with finite duality

Loten, Cynthia; Tardif, Claude

doi:10.1016/j.ejc.2007.11.007

Cited by 7 publications

(9 citation statements)

References 7 publications

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“…Since T is a core, f • g is an automorphism. By [4], Lemma 2.4, T is rigid, hence f • g is the identity on T. Therefore g must map every element u of T to an element of f −1 (u). In particular, the non-leaf u 1 ∈ S cannot be mapped to the leaf (u 1 , 1) of C 1 , so g(u 1 ) must be the copy of u 1 in T 1 .…”

Section: Untangled Sets and Degrees Of Monstrositymentioning

confidence: 99%

“…The caterpillars of [4] are the trees T such that µ(T) ≤ 2, and by [4], Corollary 4.3, these are the minimal obstructions of the core structures with finite duality which admit a near-unanimity polymorphism of arity 3. In the next section, we will show that for every integer k ≥ 2, the trees with degree of monstrosity at most k are the minimal obstructions of the core structures with finite duality which admit a near-unanimity polymorphism of arity k + 1.…”

Section: Untangled Sets and Degrees Of Monstrositymentioning

confidence: 99%

“…In [4], we gave a characterisation of the core structures with finite duality which admit majority polymorphisms, in terms of a combinatorial description of their minimal obstructions as "caterpillars". This "caterpillar duality" was formalised through datalog by Carvalho, Dalmau and Krokhin [1].…”

Section: Introductionmentioning

confidence: 99%

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Near-Unanimity Polymorphisms on Structures with Finite Duality

Loten¹,

Tardif²

2011

SIAM J. Discrete Math.

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Abstract. We introduce a combinatorial parameter on finite relational trees, called the degree of monstrosity, which measures the smallest possible arity of a near-unanimity polymorphism on a core structure with finite duality. We also show that the core structures which admit all conservative operations as polymorphisms are essentially the structures with finite duality whose minimal obstructions are trees with degree of monstrosity at most one.

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Section: Untangled Sets and Degrees Of Monstrositymentioning

confidence: 99%

Section: Untangled Sets and Degrees Of Monstrositymentioning

confidence: 99%

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Near-Unanimity Polymorphisms on Structures with Finite Duality

Loten¹,

Tardif²

2011

SIAM J. Discrete Math.

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“…In graph theory, a caterpillar is a tree which becomes a path after all its leaves are removed. Following [Loten and Tardif 2008], we say that a tree is a caterpillar if each of its blocks is incident to at most two nonleaf elements, and each element is incident to at most two non-pendant blocks. Informally, a caterpillar has a body consisting of a chain of elements v 1 , .…”

Section: Caterpillar and Jellyfish Dualitiesmentioning

confidence: 99%

Robust Satisfiability for CSPs

Dalmau

Krokhin

2013

ACM Trans. Comput. Theory

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The full-text may be used and/or reproduced, and given to third parties in any format or medium, without prior permission or charge, for personal research or study, educational, or not-for-prot purposes provided that:• a full bibliographic reference is made to the original source • a link is made to the metadata record in DRO • the full-text is not changed in any way The full-text must not be sold in any format or medium without the formal permission of the copyright holders.Please consult the full DRO policy for further details. An algorithm for a constraint satisfaction problem is called robust if it outputs an assignment satisfying at least a (1−f (ϵ))-fraction of constraints for each (1−ϵ)-satisfiable instance (i.e. such that at most a ϵ-fraction of constraints needs to be removed to make the instance satisfiable), where f (ϵ) → 0 as ϵ → 0. We establish an algebraic framework for analyzing constraint satisfaction problems admitting an efficient robust algorithm with functions f of a given growth rate. We use this framework to derive hardness results. We also describe three classes of problems admitting an efficient robust algorithm such that f is O(1/ log (1/ϵ)), O(ϵ 1/k ) for some k > 1, and O(ϵ), respectively. Finally, we give a complete classification of robust satisfiability with a given f for the Boolean case.

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“…Following [30], we say that a τ -tree is a τ -caterpillar (or simply a caterpillar) if each of its blocks is incident to at most two non-leaf elements, and each element is incident to at most two non-pendant blocks. Informally, a τ -caterpillar has a body consisting of a chain of elements a 1 , .…”

Section: Basic Definitionsmentioning

confidence: 99%

Two new homomorphism dualities and lattice operations

Carvalho

Dalmau

Krokhin

2010

Journal of Logic and Computation

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The study of constraint satisfaction problems definable in various fragments of Datalog has recently gained considerable importance. We consider constraint satisfaction problems that are definable in the smallest natural recursive fragment of Datalog -monadic linear Datalog with at most one EDB per rule, and also in the smallest non-linear extension of this fragment. We give combinatorial and algebraic characterisations of such problems, in terms of homomorphism dualities and lattice operations, respectively. We then apply our results to study graph H-colouring problems.

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Majority functions on structures with finite duality

Cited by 7 publications

References 7 publications

Near-Unanimity Polymorphisms on Structures with Finite Duality

Near-Unanimity Polymorphisms on Structures with Finite Duality

Robust Satisfiability for CSPs

Two new homomorphism dualities and lattice operations

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