Representing and computing regular languages on massively parallelnetworks
Miller, M.I.; Roysam, B.; Smith, K.R.; Oapos;Sullivan, J.A.
Neural Networks, IEEE Transactions on
Volume 2, Issue 1, Jan 1991 Page(s):56 - 72
Digital Object Identifier 10.1109/72.80291
Summary:A general method is proposed for incorporating rule-based
constraints corresponding to regular languages into stochastic inference
problems, thereby allowing for a unified representation of stochastic
and syntactic pattern constraints. The authors' approach establishes the
formal connection of rules to Chomsky grammars and generalizes the
original work of Shannon on the encoding of rule-based channel sequences
to Markov chains of maximum entropy. This maximum entropy probabilistic
view leads to Gibbs representations with potentials which have their
number of minima growing at precisely the exponential rate that the
language of deterministically constrained sequences grow. These
representations are coupled to stochastic diffusion algorithms, which
sample the language-constrained sequences by visiting the energy minima
according to the underlying Gibbs probability law. This coupling yields
the result that fully parallel stochastic cellular automata can be
derived to generate samples from the rule-based constraint sets. The
production rules and neighborhood state structure of the language of
sequences directly determine the necessary connection structures of the
required parallel computing surface. Representations of this type have
been mapped to the DAP-510 massively parallel processor consisting of
1024 mesh-connected bit-serial processing elements for performing
automated segmentation of electron-micrograph images
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