Lars Engebretsen

We show that the k-CSP problem over a finite Abelian group G

cannot be approximated within |G|^{k-O(sqrt{k})}-epsilon, for

any constant epsilon>0, unless P=NP. This lower bound matches

well with the best known upper bound, |G|^{k-1}, of Serna,

Trevisan and Xhafa. The proof uses a combination of PCP

techniques---most notably a ...
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Víctor Dalmau

We give in this paper a different and simpler proof of the tractability of Mal'tsev contraints.

more >>>Serge Gaspers, Stefan Szeider

We investigate the parameterized complexity of deciding whether a constraint network is $k$-consistent. We show that, parameterized by $k$, the problem is complete for the complexity class co-W[2]. As secondary parameters we consider the maximum domain size $d$ and the maximum number $\ell$ of constraints in which a variable occurs. ... more >>>

Jason Li, Ryan O'Donnell

We show that the basic semidefinite programming relaxation value of any constraint satisfaction problem can be computed in NC; that is, in parallel polylogarithmic time and polynomial work. As a complexity-theoretic consequence we get that MIP1$[k,c,s] \subseteq $ PSPACE provided $s/c \leq (.62-o(1))k/2^k$, resolving a question of Austrin, Håstad, and ... more >>>

Venkatesan Guruswami, Jakub Opršal, Sai Sandeep

Dinur's celebrated proof of the PCP theorem alternates two main steps in several iterations: gap amplification to increase the soundness gap by a large constant factor (at the expense of much larger alphabet size), and a composition step that brings back the alphabet size to an absolute constant (at the ... more >>>

Michal Koucky, Vojtech Rodl, Navid Talebanfard

We show that for every $r \ge 2$ there exists $\epsilon_r > 0$ such that any $r$-uniform hypergraph on $m$ edges with bounded vertex degree has a set of at most $(\frac{1}{2} - \epsilon_r)m$ edges the removal of which breaks the hypergraph into connected components with at most $m/2$ edges. ... more >>>

Dorit Aharonov, Alex Bredariol Grilo

Despite the interest in the complexity class MA, the randomized analog of NP, there is just a couple of known natural (promise-)MA-complete problems, the first due to Bravyi and Terhal (SIAM Journal of Computing 2009) and the second due to Bravyi (Quantum Information and Computation 2015). Surprisingly, both problems are ... more >>>