Mathematics
Asynchronous Distributed Processes -- the path not taken. The original work of John vonNeumann and Stan Ulam in developing a model of multi-cellular organisms fails to support the goals expressed by vonNeumann. Specifically, the final product (cellular automata) is far from biologically natural. The historical context of this mis-step, and a suggested explanation are presented. This paper was written with undergraduate mathematics major William Hughes as an undergraduate research project here at USF. Copies are available. See first page.
A New Solution
to Turing’s Leopards’ Spots Problem -- based on local entropy reduction.
A finite-state automaton exists which
-- if used as the vertices of an irregular, asynchronously active, finite
network -- will eventually generate the pattern of a leopard’s spots. This
problem was first posed and solved by Allan Turing [1955] using a model defined
in terms of [real] analysis. The solution given here is completely different.
One way of understanding the dynamics of this solution is to think of the
automata as acting to locally-reduce a Shannon entropy. A MAPLE-based simulator
is included with the theory. Some history and
pictures.
A Totally Distributed
Solution of the WakeUp Problem describes
a totally-distributed algorithm for recognizing
network recovery. The netork is assumes to be finite, asynchronous, irregular,
nets of finite-state automata -- e.g., packet-switching nets and possibly
the packet-control networks for power delivery. Recovery applies to subnets
corresponding to network tasks.
Topology and Analysis of First-Order Properties
of Asynchronous Distributed Processes. This
preprint is a full-blown presentation of the powerful analysis upon which
the results above rest. Basically, the runs of an asynchronous network of
finite-state automata are Markov chains. The space of such runs can be given
a realistic measure from which 0,1-laws are derived. In many circumstances,
these laws easily predict the global behavior of the network.
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