Sandwiches for promise constraint satisfaction

Deng, Guofeng; Sai, Ezzeddine El; Manders, Trevor; Mayr, Peter; Nakkirt, Poramate; Sparks, Athena

doi:10.1007/s00012-020-00702-5

Cited by 1 publication

(4 citation statements)

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“…In contrast we show that if A, B are graphs and PCSP(A, B) reduces to tractable CSP(C) for some finite C, then already A or B has tractable CSP. This extends results and answers a question of [8].…”

supporting

confidence: 84%

“…In contrast we show that for undirected graphs A, B, every finitely tractable PCSP(A, B) reduces to a tractable CSP(C) for a graph C of size ≤ |A| (Corollary 4.2). This answers Problem 1 of [8].…”

Section: Introductionmentioning

confidence: 58%

“…For every n > 1 and every prime p we give structures A, B of size n with a single n p -ary relation such that PCSP(A, B) reduces to a tractable CSP(C) for some sandwiched C of size p but not to a tractable CSP over any smaller sandwiched structure. For n = 2 and p = 3 such an example was given in [8].…”

Section: Big Affine Sandwichesmentioning

confidence: 99%

“…Barto [2] provided the first example of a PCSP that is tractable but not finitely tractable. In [8] the second author of this paper and his students gave the first example of a finitely tractable PCSP(A, B) for A, B of size 2 that does not reduce to a tractable CSP(C) for any C of size ≤ 2.…”

Section: Introductionmentioning

confidence: 99%

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Small Promise CSPs that reduce to large CSPs

Kazda¹,

Mayr²,

Zhuk³

2021

Preprint

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For relational structures A, B of the same signature, the Promise Constraint Satisfaction Problem PCSP(A, B) asks whether a given input structure maps homomorphically to A or does not even map to B. We are promised that the input satisfies exactly one of these two cases.If there exists a structure C with homomorphisms A → C → B, then PCSP(A, B) reduces naturally to CSP(C). To the best of our knowledge all known tractable PCSPs reduce to tractable CSPs in this way. However Barto [2] showed that some PCSPs over finite structures A, B require solving CSPs over infinite C.We show that even when such a reduction to finite C is possible, this structure may become arbitrarily large. For every integer n > 1 and every prime p we give A, B of size n with a single relation of arity n p such that PCSP(A, B) reduces via a chain of homomorphisms A → C → B to a tractable CSP over some C of size p but not over any smaller structure. In a second family of examples, for every prime p ≥ 7 we construct A, B of size p − 1 with a single ternary relation such that PCSP(A, B) reduces via A → C → B to a tractable CSP over some C of size p but not over any smaller structure. In contrast we show that if A, B are graphs and PCSP(A, B) reduces to tractable CSP(C) for some finite C, then already A or B has tractable CSP. This extends results and answers a question of [8].

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supporting

confidence: 84%

Section: Introductionmentioning

confidence: 58%

Section: Big Affine Sandwichesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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