We introduce a model for analog computation with discrete
time in the presence of analog noise
that is flexible enough to cover the most important concrete
cases, such as noisy analog neural nets and networks of spiking neurons.
This model subsumes the classical ... more >>>

We consider recurrent analog neural nets where the output of each
gate is subject to Gaussian noise, or any other common noise
distribution that is nonzero on a large set.
We show that many regular languages cannot be recognized by
networks of this type, and
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Using a new statistical embedding of words which has similarities with the Parikh mapping, we first construct a tolerant tester for the equality of two words, whose complexity is independent of the string size, where the distance between inputs is measured by the normalized edit distance with moves. As a ... more >>>

We consider the regular languages recognized by weighted threshold circuits with a linear number of wires.
We present a simple proof to show that parity cannot be computed by such circuits.
Our proofs are based on an explicit construction to restrict the input of the circuit such that the value ... more >>>