Constraint Satisfaction Problems over Finite Structures

@article{Barto2021ConstraintSP,
  title={Constraint Satisfaction Problems over Finite Structures},
  author={Libor Barto and William DeMeo and Antoine Mottet},
  journal={2021 36th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)},
  year={2021},
  pages={1-13}
}
We initiate a systematic study of the computational complexity of the Constraint Satisfaction Problem (CSP) over finite structures that may contain both relations and operations. We show the close connection between this problem and a natural algebraic question: which finite algebras admit only polynomially many homomorphisms into them?We give some sufficient and some necessary conditions for a finite algebra to have this property. In particular, we show that every finite equationally… 

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