A new holant dichotomy inspired by quantum computation

Miriam Backens*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

9 Citations (Scopus)
34 Downloads (Pure)


Holant problems are a framework for the analysis of counting complexity problems on graphs. This framework is simultaneously general enough to encompass many counting problems on graphs and specific enough to allow the derivation of dichotomy results, partitioning all problems into those which are in FP and those which are #P-hard. The Holant framework is based on the theory of holographic algorithms, which was originally inspired by concepts from quantum computation, but this connection appears not to have been explored before. Here, we employ quantum information theory to explain existing results in a concise way and to derive a dichotomy for a new family of problems, which we call Holant+. This family sits in between the known families of Holant∗, for which a full dichotomy is known, and Holantc, for which only a restricted dichotomy is known. Using knowledge from entanglement theory - both previously existing work and new results of our own - we prove a full dichotomy theorem for Holant+, which is very similar to the restricted Holantc dichotomy and may thus be a stepping stone to a full dichotomy for that family.

Original languageEnglish
Title of host publication44th International Colloquium on Automata, Languages, and Programming, ICALP 2017
EditorsAnca Muscholl, Piotr Indyk, Fabian Kuhn, Ioannis Chatzigiannakis
PublisherSchloss Dagstuhl
Number of pages14
ISBN (Electronic)978-3-95977-041-5
Publication statusPublished - 14 Jul 2017
Event44th International Colloquium on Automata, Languages, and Programming, ICALP 2017 - Warsaw, Poland
Duration: 10 Jul 201714 Jul 2017

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference44th International Colloquium on Automata, Languages, and Programming, ICALP 2017


  • Computational complexity
  • Counting complexity
  • Dichotomy
  • Entanglement
  • Holant

ASJC Scopus subject areas

  • Software


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