On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction
The universal-algebraic approach has proved a powerful tool in the study of the complexity of CSPs. This approach has previously been applied to the study of CSPs with finite or (infinite) omega-categorical templates, and relies on two facts. The first is that in finite or omega-categorical structur...
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| Format: | Article |
| Language: | English |
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Logical Methods in Computer Science e.V.
2012-09-01
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| Series: | Logical Methods in Computer Science |
| Subjects: | |
| Online Access: | https://lmcs.episciences.org/674/pdf |
| _version_ | 1797268673088454656 |
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| author | Barnaby Martin Manuel Bodirsky Martin Hils |
| author_facet | Barnaby Martin Manuel Bodirsky Martin Hils |
| author_sort | Barnaby Martin |
| collection | DOAJ |
| description | The universal-algebraic approach has proved a powerful tool in the study of
the complexity of CSPs. This approach has previously been applied to the study
of CSPs with finite or (infinite) omega-categorical templates, and relies on
two facts. The first is that in finite or omega-categorical structures A, a
relation is primitive positive definable if and only if it is preserved by the
polymorphisms of A. The second is that every finite or omega-categorical
structure is homomorphically equivalent to a core structure. In this paper, we
present generalizations of these facts to infinite structures that are not
necessarily omega-categorical. (This abstract has been severely curtailed by
the space constraints of arXiv -- please read the full abstract in the
article.) Finally, we present applications of our general results to the
description and analysis of the complexity of CSPs. In particular, we give
general hardness criteria based on the absence of polymorphisms that depend on
more than one argument, and we present a polymorphism-based description of
those CSPs that are first-order definable (and therefore can be solved in
polynomial time). |
| first_indexed | 2024-04-25T01:36:13Z |
| format | Article |
| id | doaj.art-025db35ff4d9422a921ec79672e4a245 |
| institution | Directory Open Access Journal |
| issn | 1860-5974 |
| language | English |
| last_indexed | 2024-04-25T01:36:13Z |
| publishDate | 2012-09-01 |
| publisher | Logical Methods in Computer Science e.V. |
| record_format | Article |
| series | Logical Methods in Computer Science |
| spelling | doaj.art-025db35ff4d9422a921ec79672e4a2452024-03-08T09:28:00ZengLogical Methods in Computer Science e.V.Logical Methods in Computer Science1860-59742012-09-01Volume 8, Issue 310.2168/LMCS-8(3:13)2012674On the Scope of the Universal-Algebraic Approach to Constraint SatisfactionBarnaby Martinhttps://orcid.org/0000-0002-4642-8614Manuel Bodirskyhttps://orcid.org/0000-0001-8228-3611Martin Hilshttps://orcid.org/0000-0002-4304-288XThe universal-algebraic approach has proved a powerful tool in the study of the complexity of CSPs. This approach has previously been applied to the study of CSPs with finite or (infinite) omega-categorical templates, and relies on two facts. The first is that in finite or omega-categorical structures A, a relation is primitive positive definable if and only if it is preserved by the polymorphisms of A. The second is that every finite or omega-categorical structure is homomorphically equivalent to a core structure. In this paper, we present generalizations of these facts to infinite structures that are not necessarily omega-categorical. (This abstract has been severely curtailed by the space constraints of arXiv -- please read the full abstract in the article.) Finally, we present applications of our general results to the description and analysis of the complexity of CSPs. In particular, we give general hardness criteria based on the absence of polymorphisms that depend on more than one argument, and we present a polymorphism-based description of those CSPs that are first-order definable (and therefore can be solved in polynomial time).https://lmcs.episciences.org/674/pdfcomputer science - logic in computer sciencecomputer science - artificial intelligencecomputer science - computational complexity |
| spellingShingle | Barnaby Martin Manuel Bodirsky Martin Hils On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction Logical Methods in Computer Science computer science - logic in computer science computer science - artificial intelligence computer science - computational complexity |
| title | On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction |
| title_full | On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction |
| title_fullStr | On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction |
| title_full_unstemmed | On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction |
| title_short | On the Scope of the Universal-Algebraic Approach to Constraint Satisfaction |
| title_sort | on the scope of the universal algebraic approach to constraint satisfaction |
| topic | computer science - logic in computer science computer science - artificial intelligence computer science - computational complexity |
| url | https://lmcs.episciences.org/674/pdf |
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