SOME UNIVERSAL ELEMENTS FOR FINITE AUTOMATA
FIGURE 5
the pulse does depend on the stimulus, and a device similar to part III of
the ’’unit pulser" (section 0 above) can be constructed to remedy this. In
the "shifting" device above a similar method must be used.
Both con-junctions and dis-junctions are realizable with a single
copy of the McCulloch-Pitts element
and if this element is provided with a refractory period, it becomes an
essentially universal element, by itself. The same is true for the element
since con-junction (with del^y 2 ) can be obtained in the form
— r ^ -
The former of these two universal elements may have some interest in con
nection with brain theory inasmuch as it shows that, generally speaking,
tne rather weak property of having a refractory period is sufficient, in
principle, to account for physiological phenomena which might superficially
appear to show a "more strongly non-monotonic" character such as "inhibition."
The hypothesis that "con-junctions” and "dis-junctions" are initially
available is motivated by the prevailing opinion in neurophysiology that such
elements are almost certainly represented among, and in fact are probably
characteristic of, the cells of the central nervous system. On the other
hand, the nature and distribution of the non-monotonic properties of the
nervous system are not nearly so well understood, in particular the various
forms of "inhibition". Thus the particular form of the theorem may be of
some value in analysing those neural phenomena In which there appears to be
an "inhibitory" quality but in which no specific inhibitory connection or
mechanism has been isolated. The neuro-physiologist should be aware of the
fact that the element of Figure 6 , in particular, is universal, since it
MINSKY
would not be rash to conjecture that a very large proportion of central
nervous cells have some properties like those of this configuration, or dif
fering only quantitatively. It is not my intention to suggest that the
particular nets constructed for this proof bear any resemblance to mechanisms
to be found in the central nervous system; their form reflects primarily the
"reduction to canonical form" which is the major mathematical and logical
tool used for the proof of the main theorem. To realize any particular
response function, there are many other nets that could be used, not a few
of which would be much more efficient in the number of elements used and per
haps much less orderly in appearance. It is perhaps worth adding that there
would appear to be no reason why the recent results of von Neumann and Shannon
on automata with "probabilistic" or "unreliable" elements could not be applied
to the constructions of the present paper to satisfy the biological critic
that the validity of the main theorem does not at all rest on what might be
felt to be a perfection of hypothetical elements that could not mirror any
biological situation.
Society of Fellows,
Harvard University.
BIBLIOGRAPHY
Most of this material is derived from Chapter II of my disserta
tion; the results there are in slightly more general form.
[1] CURRY, H. B., No specific reference is intended but see e. g., Am. J.
Math., Vol. 52, 509 ff., T89 ff.
[
2
] KLEENE, S . C ., See this volume.
[3] McCULLOCH, W. S. and PITTS, W.,
19
*
0
, "A Logical Calculus of the Ideas
Immanent in Nervous Activity," Bull. Math. Biophysics, 5, 115 ff.
[h] MINSKY. M. L., Neural-Analog Networks and the Brain-Model Problem,
Princeton University, 1954. This Is not in print, but microfilm copies
are available. A revision is in preparation for publication.
[5] von NEUMANN, J., See this volume.
[6 ] RASHEVSKY, N., 1938. Mathematical Biophysics. Univ. of Chicago Press.
[7 ] SHANNON, C. E., See this volume.
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