  We have calculated the key characteristics of associative
(content-addressable) spatial-temporal memories based on neuromorphic networks
with restricted connectivity - "CrossNets". Such networks may be naturally
implemented in nanoelectronic hardware using hybrid CMOS/memristor circuits,
which may feature extremely high energy efficiency, approaching that of
biological cortical circuits, at much higher operation speed. Our numerical
simulations, in some cases confirmed by analytical calculations, have shown
that the characteristics depend substantially on the method of information
recording into the memory. Of the four methods we have explored, two look
especially promising - one based on the quadratic programming, and the other
one being a specific discrete version of the gradient descent. The latter
method provides a slightly lower memory capacity (at the same fidelity) then
the former one, but it allows local recording, which may be more readily
implemented in nanoelectronic hardware. Most importantly, at the synchronous
retrieval, both methods provide a capacity higher than that of the well-known
Ternary Content-Addressable Memories with the same number of nonvolatile memory
cells (e.g., memristors), though the input noise immunity of the CrossNet
memories is somewhat lower.
