A series of recent works have established the dichotomy of general-valued constraint satisfaction problems (VCSPs): every VCSP language can either be solved in polynomial time or is NP-hard. I will describe the algorithmic part of this dichotomy. As a key subroutine, we use a polynomial-time algorithm for ordinary CSPs satisfying a certain algebraic condition, whose existence was proved by Bulatov and by Zhuk in 2017. Joint work with Andrei Krokhin and Michal Rolinek (http://pub.ist.ac.at/~vnk/papers/VCSP.html ).
Shunsuke Tsuchioka (Tokyo Institute of Technology)
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We generalize the theory of linked partition ideals due to Andrews using finite automata in formal language theory and apply it to prove three Rogers-Ramanujan type identities of modulo 14 that were posed by Nandi through vertex operator theoretic construction of the level 4 standard modules of the affine Lie algebra . This is a joint work with Motoki Takigiku.