11 papers
Equations over Finite Monoids with Infinite Promises
Alberto Larrauri, Antoine Mottet, Stanislav Živný +1
Larrauri and Živný [ICALP'25/ACM ToCL'24] recently established a complete complexity classification of the problem of solving a system of equations over a monoid assuming that…
Optimal Inapproximability of Promise Equations over Finite Groups
Silvia Butti, Alberto Larrauri, Stanislav Živný
A celebrated result of Hastad established that, for any constant , it is NP-hard to find an assignment satisfying a -fraction of the constraints…
Counting Answers to Unions of Conjunctive Queries: Natural Tractability Criteria and Meta-Complexity
Jacob Focke, Leslie Ann Goldberg, Marc Roth +1
We study the problem of counting answers to unions of conjunctive queries (UCQs) under structural restrictions on the input query. Concretely, given a class C of UCQs, the problem…
Satisfiability of commutative vs. non-commutative CSPs
Andrei A. Bulatov, Stanislav Živný
The Mermin-Peres magic square is a celebrated example of a system of Boolean linear equations that is not (classically) satisfiable but is satisfiable via linear operators on a Hil…
A logarithmic approximation of linearly ordered colourings
Johan Håstad, Björn Martinsson, Tamio-Vesa Nakajima +1
A linearly ordered (LO) -colouring of a hypergraph assigns to each vertex a colour from the set in such a way that each hyperedge has a unique maximum eleme…
Approximate Graph Colouring and the Crystal with a Hollow Shadow
Lorenzo Ciardo, Stanislav Živný
We show that approximate graph colouring is not solved by the lift-and-project hierarchy for the combination of linear programming and linear Diophantine equations. The proof is ba…