Hyper-finite-state automaton
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A Hyper-finite-state automaton or Hyper-finite-state machine is a generalization of a Finite-state automaton (which can be represented as a directed graph) that can be represented as a directed hypergraph. It is suspected that there is more than one way to implement this, so this page doesn't bother to define just one; it lists possible HFSM designs.
Concurrent HFSM
One model of a Hyper-finite-state machine is to allow a normal Finite State Machine to be concurrent by making it so that, when a node follows to another node from a particular (hyper)edge, it goes to multiple states (all state that the hyperedge points to). This makes the Hyper-finite-state-machine similar to a Neural Network.