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dc.contributor.authorCarvalho, Catarina
dc.contributor.authorMadelaine, Florent
dc.contributor.authorMartin, Barnaby
dc.date.accessioned2017-01-19T18:06:27Z
dc.date.available2017-01-19T18:06:27Z
dc.date.issued2015-08-03
dc.identifier.citationCarvalho , C , Madelaine , F & Martin , B 2015 , From complexity to algebra and back: digraph classes, collapsibility and the PGP . in Proceedings of the 2015 30th Annual ACM / IEEE Symposium on logic in Computer Science (LICS) . IEEE , pp. 462-474 , 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2015) , Kyoto , Japan , 6/07/15 . https://doi.org/10.1109/LICS.2015.50
dc.identifier.citationconference
dc.identifier.isbn1043-6871
dc.identifier.otherPURE: 10920723
dc.identifier.otherPURE UUID: 98d3bbb0-d795-4ddf-acda-a0e5b80a00ef
dc.identifier.otherScopus: 84945913469
dc.identifier.otherORCID: /0000-0002-4648-7016/work/62748315
dc.identifier.urihttp://hdl.handle.net/2299/17536
dc.descriptionThis is the accepted version of the following article: C. Carvalho, M. Florent, & M. Barnaby, “Fom complexity to algebra and back: digraph classes, collapsibility, and the PGP”, published in Proceedings of the 2015 30th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 6-10 July 2015, IEEE Xplore Digital Library, August 2015. The final, published version is available online via doi: 10.1109/LICS.2015.50 © 2015 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works.
dc.description.abstractInspired by computational complexity results for the quantified constraint satisfaction problem, we study the clones of idem potent polymorphisms of certain digraph classes. Our first results are two algebraic dichotomy, even "gap", theorems. Building on and extending [Martin CP'11], we prove that partially reflexive paths bequeath a set of idem potent polymorphisms whose associated clone algebra has: either the polynomially generated powers property (PGP), or the exponentially generated powers property (EGP). Similarly, we build on [DaMM ICALP'14] to prove that semi complete digraphs have the same property. These gap theorems are further motivated by new evidence that PGP could be the algebraic explanation that a QCSP is in NP even for unbounded alternation. Along the way we also effect a study of a concrete form of PGP known as collapsibility, tying together the algebraic and structural threads from [Chen Sicomp'08], and show that collapsibility is equivalent to its Pi2-restriction. We also give a decision procedure for k-collapsibility from a singleton source of a finite structure (a form of collapsibility which covers all known examples of PGP for finite structures). Finally, we present a new QCSP trichotomy result, for partially reflexive paths with constants. Without constants it is known these QCSPs are either in NL or Pspace-complete [Martin CP'11], but we prove that with constants they attain the three complexities NL, NP-complete and Pspace-complete.en
dc.format.extent13
dc.language.isoeng
dc.publisherIEEE
dc.relation.ispartofProceedings of the 2015 30th Annual ACM / IEEE Symposium on logic in Computer Science (LICS)
dc.subjectalgebra
dc.subjectcomplexity theory
dc.subjectcloning
dc.subjectpolynomials
dc.subjectelectronic mail
dc.subjectconcrete
dc.titleFrom complexity to algebra and back: : digraph classes, collapsibility and the PGPen
dc.contributor.institutionSchool of Physics, Astronomy and Mathematics
dc.contributor.institutionCentre for Computer Science and Informatics Research
dc.contributor.institutionScience & Technology Research Institute
rioxxterms.versionAM
rioxxterms.versionofrecordhttps://doi.org/10.1109/LICS.2015.50
rioxxterms.typeOther
herts.preservation.rarelyaccessedtrue


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