Endre søk
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf
From Holant to #CSP and Back: Dichotomy for Holant (c) Problems
KTH, Skolan för datavetenskap och kommunikation (CSC), Teoretisk datalogi, TCS.ORCID-id: 0000-0002-1600-5290
2012 (engelsk)Inngår i: Algorithmica, ISSN 0178-4617, E-ISSN 1432-0541, Vol. 64, nr 3, s. 511-533Artikkel i tidsskrift (Fagfellevurdert) Published
Abstract [en]

We explore the intricate interdependent relationship among counting problems, considered from three frameworks for such problems: Holant Problems, counting CSP and weighted H-colorings. We consider these problems for general complex valued functions that take boolean inputs. We show that results from one framework can be used to derive results in another, and this happens in both directions. Holographic reductions discover an underlying unity, which is only revealed when these counting problems are investigated in the complex domain a",. We prove three complexity dichotomy theorems, leading to a general theorem for Holant (c) problems. This is the natural class of Holant problems where one can assign constants 0 or 1. More specifically, given any signature grid on G=(V,E) over a set of symmetric functions, we completely classify the complexity to be in P or #P-hard, according to F , of Sigma Pi f(v)(sigma vertical bar E(v)), sigma:E ->{0,1}v epsilon V where f(v) epsilon F boolean OR {0, 1} (0, 1 are the unary constant 0, 1 functions). Not only is holographic reduction the main tool, but also the final dichotomy can be only naturally stated in the language of holographic transformations. The proof goes through another dichotomy theorem on Boolean complex weighted #CSP.

sted, utgiver, år, opplag, sider
2012. Vol. 64, nr 3, s. 511-533
Emneord [en]
Holant problem, #CSP, Holographic reduction, Dichotomy
HSV kategori
Identifikatorer
URN: urn:nbn:se:kth:diva-103121DOI: 10.1007/s00453-012-9626-6ISI: 000308228400009Scopus ID: 2-s2.0-84867229589OAI: oai:DiVA.org:kth-103121DiVA, id: diva2:558710
Merknad

QC 20121004

Tilgjengelig fra: 2012-10-04 Laget: 2012-10-04 Sist oppdatert: 2022-06-24bibliografisk kontrollert

Open Access i DiVA

Fulltekst mangler i DiVA

Andre lenker

Forlagets fulltekstScopus

Person

Huang, Sangxia

Søk i DiVA

Av forfatter/redaktør
Huang, Sangxia
Av organisasjonen
I samme tidsskrift
Algorithmica

Søk utenfor DiVA

GoogleGoogle Scholar

doi
urn-nbn

Altmetric

doi
urn-nbn
Totalt: 101 treff
RefereraExporteraLink to record
Permanent link

Direct link
Referera
Referensformat
  • apa
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Annet format
Fler format
Språk
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Annet språk
Fler språk
Utmatningsformat
  • html
  • text
  • asciidoc
  • rtf