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Algebraic Theory of Promise Constraint Satisfaction Problems, First Steps

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Fundamentals of Computation Theory (FCT 2019)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11651))

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Abstract

What makes a computational problem easy (e.g., in P, that is, solvable in polynomial time) or hard (e.g., NP-hard)? This fundamental question now has a satisfactory answer for a quite broad class of computational problems, so called fixed-template constraint satisfaction problems (CSPs) – it has turned out that their complexity is captured by a certain specific form of symmetry. This paper explains an extension of this theory to a much broader class of computational problems, the promise CSPs, which includes relaxed versions of CSPs such as the problem of finding a 137-coloring of a 3-colorable graph.

Libor Barto has received funding from the European Research Council (ERC) under the European Unions Horizon 2020 research and innovation programme (grant agreement No 771005).

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Notes

  1. 1.

    Here we should rather say a hypergraph whose hyperedges have size at most 3 because of conjuncts of the form \(3NAE_k(x,x,y)\) or \(3NAE_k(x,x,x)\). Let us ignore this minor technical imprecision.

  2. 2.

    Their conjecture is equivalent but was, of course, originally stated in a different language – the significance of minor conditions in CSPs was identified much later.

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Authors and Affiliations

  1. Department of Algebra, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 18675, Praha 8, Czechia

    Libor Barto

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  1. Libor Barto
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  1. University of Liverpool, Liverpool, UK

    Leszek Antoni Gąsieniec

  2. Hong Kong Polytechnic University, Hong Kong, China

    Jesper Jansson

  3. Lund University, Lund, Sweden

    Christos Levcopoulos

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Barto, L. (2019). Algebraic Theory of Promise Constraint Satisfaction Problems, First Steps. In: Gąsieniec, L., Jansson, J., Levcopoulos, C. (eds) Fundamentals of Computation Theory. FCT 2019. Lecture Notes in Computer Science(), vol 11651. Springer, Cham. https://doi.org/10.1007/978-3-030-25027-0_1

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  • DOI: https://doi.org/10.1007/978-3-030-25027-0_1

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