This article studies the computational power of various discontinuous real computational models that are based on the classical analog recur- rent neural network (ARNN). This ARNN consists of finite number of neurons; each neuron computes a polynomial net function and a sigmoid- like continuous activation function. We introduce arithmetic networks as ARNN augmented with a few simple discontinuous (e. g., threshold or Zero test) neurons. We argue that even with weights restricted to poly- Nomial time computable reals, arithmetic networks are able to compute Arbitrarily complex recursive functions.
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