2007
DOI: 10.1007/s00012-007-2012-6
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Bounded width problems and algebras

Abstract: Let A be finite relational structure of finite type, and let CSP (A) denote the following decision problem: if I is a given structure of the same type as A, is there a homomorphism from I to A? To each relational structure A is associated naturally an algebra A whose structure determines the complexity of the associated decision problem. We investigate those finite algebras arising from CSP's of so-called bounded width, i.e., for which local consistency algorithms effectively decide the problem. We show that i… Show more

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Cited by 84 publications
(78 citation statements)
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“…No language which can, in some sense, simulate q-LIN has thus bounded relational width [18]. In [1,4], it was proved that this is the only obstacle in case of finite languages.…”
mentioning
confidence: 99%
“…No language which can, in some sense, simulate q-LIN has thus bounded relational width [18]. In [1,4], it was proved that this is the only obstacle in case of finite languages.…”
mentioning
confidence: 99%
“…In the above theorem, the necessity of condition (1) was proved in [49], and the equivalence of conditions (1) and (2) in [51].…”
Section: Theorem 26 ([49])mentioning
confidence: 93%
“…Note that we use two numbers to parameterise treewidth and pathwidth, as is customary in the study of CSPs [16,22,49] (rather than one as is customary in graph theory [28]), for the following reason. The first parameter j gives a more convenient parameterization of CSPs, since the second parameter k is bounded from below by the maximum arity of a relation in a structure, and hence it is less convenient to use for uniform treatment of structures of different vocabularies that behave essentially in the same way with respect to homomorphisms.…”
Section: Obstructions and Dualitiesmentioning
confidence: 99%
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“…The following theorem relates polymorphisms, complexity, and expressibility in Datalog Theorem 1 ( [29,31,35]). Let H 1 and H 2 be two structures with a common universe.…”
Section: Example 3 ([40]mentioning
confidence: 99%