A Dichotomy for Real Boolean Holant Problems

Abstract: Abstract: In this talk, we present a complexity dichotomy for Holant problems on the boolean domain with arbitrary sets of real-valued constraint functions. These constraint functions need not be symmetric nor do we assume any auxiliary functions as in previous results. It is proved that for every set F of real-valued constraint functions, Holant(F) is either P-time computable or #P-hard. The classification has an explicit criterion. This is a culmination of much research on a decade-long classification program for Holant problems, and it uses previous results and techniques from many researchers. However, as it turned out, the journey to the present theorem has been arduous. Some particularly intriguing concrete functions f6, f8 and their associated families with extraordinary closure properties related to Bell states in quantum information theory play an important role in this proof.

Based on joint work with Jin-Yi Cai.

computational complexitycomputational geometrycryptography and securitydiscrete mathematicsdata structures and algorithmsgame theorymachine learningquantum computing and informationcombinatoricsinformation theoryoptimization and controlprobability

Audience: researchers in the topic

TCS+

Series comments: Description: Theoretical Computer Science

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