On Symmetric Circuits and Fixed-Point Logics

@article{Anderson2014OnSC,
  title={On Symmetric Circuits and Fixed-Point Logics},
  author={Matthew Anderson and Anuj Dawar},
  journal={Theory of Computing Systems},
  year={2014},
  volume={60},
  pages={521-551}
}
We study properties of relational structures, such as graphs, that are decided by families of Boolean circuits. Circuits that decide such properties are necessarily invariant to permutations of the elements of the input structures. We focus on families of circuits that are symmetric, i.e., circuits whose invariance is witnessed by automorphisms of the circuit induced by the permutation of the input structure. We show that the expressive power of such families is closely tied to definability in… CONTINUE READING