Abstract. In
the
mathematical domain of algorithmic information theory (AIT), randomness
is defined to mean so much as the absence of regularity. Accordingly, a
simplest code of a symbol string is taken to
be a code that squeezes out a maximum amount of regularity. This
implies, in AIT, that simplest codes of symbol strings are
incomputable, because one
can never be sure that a maximum amount of regularity has been squeezed
out.
But, what is regularity? This question has been addressed in the
perceptual domain of structural information theory (SIT), resulting in
a definition of regularity that seems relevant not only in visual
perception but also in, for instance, molecular biology. This
definition leads to a coding language in which, basically, only three
kinds of regularity are taken into account. Within this perceptual
coding theory, the set of symbol strings that may represent a given
object is still incomputable, but simplest codes of given symbol
strings are computable. That is, SIT's definition of regularity allows
for so-called transparallel processing, which means that an exponential
number of codes can be dealt with as if only one code were concerned.
Peter
A. van der Helm 