We report the first exhaustive enumeration of all Boolean feedback topologies with up to five two-input gates under both synchronous and asynchronous dynamics (4. 18×10⁹ topologies). Error correction, where every single-bit perturbation of every attractor is dynamically absorbed, requires K = 5 gates synchronously and K = 4 asynchronously, and the two solution sets are completely disjoint: zero circuits correct under both modes. The populations exhibit structural inversion: synchronous hits require mutual feedback pairs and zero self-loops; asynchronous hits require self-loops and zero mutual pairs. We prove that one-step correction is impossible for any K, and find that all error-correcting circuits store exactly one bit. The update mode of a feedback network is a fundamental determinant of its error-correctingarchitecture.
Amos Weiskopf (Tue,) studied this question.