Symmetry and First-order: Explicitly Presentation-invariant Circuits
نویسنده
چکیده
We investigate circuit complexity under the additional assumption of full combinatorial symmetry with respect to permutations of the input representation. With this approach we derive a very natural and simple characterization of rst-order logic and its innnitary variant with bounded numbers of variables over nite structures. Extending these results to not necessarily acyclic boolean networks, we derive corresponding characterizations of partial xed-point logic (or the relational query language WHILE) and ordinary xed-point logic.
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