output Venn, and place jot(s) in the output Venn of that neuron of the Then, look at the AB space of the Venn in the neuron of the second Then, pass to the ~A~3 space of the Venn in the neuron of the second rank. Carry out the same procedure as above by searching for those community sets which have no jots in corresponding spaces of the two output Venns of the first rank. Then pass to the A-B space of the Venn in the neuron and continue as above by searching for those community sets of the first rank which have a jot in the space of the right output Venn and no jot in the space of the left output Venn. 3. The output of a neuron in the third rank is computed in the same way as the output of a neuron of the second rank. Errors in Nets: This procedure is easily generalized to all values of (fig. 8). Several types of nets have been investigated. We can only mention them and give a few examples. The interested reader is referred to several fine papers on the subject. A LOGICALLY STABLE NET is a net in which the neurons change threshold simultaneously (4). An example is given in figure 7. We have found it is always possible to construct a logically stable net to compute any desired function for (1-2).102% range of threshold of the component neurons. We have also found the exact range of threshold that neurons in a logically stable net may have when the logical functions in Venn form, computed by each and every neuron, are constrained to have the same number of jots. As a simple bound, we can show that for ≥ 3, a range of chreshold of (1-1/8 ).102% is always obtainable. Nets of neurons having thresholds which fluctuate independently of each other have been studied by Gene Prange of the Cambridge Air Force Research Center. He has obtained bounds on the permissible fluctuations of threshold of the neurons in a net which computes an error-free output. These bounds are for all d We use his notation in figure 8 where jots, blanks and dashes in a Venn diagram represent respectively input configurations for which the neuron always fires, never fires or fires with error. Figure 7. Mc Culloch net, logically stable over 75% of range of threshold. W. S. McCulloch has studied changes in signal strength and in synapsis of fibers to a neuron (5). This includes the possibility of error due to faulty connections of the fibers to a neuron. Another means of studying this type of error, proposed by Jack Cowan, is to view the arrangement of fibers to a neuron as Leo Verbeek, whose paper appears in this volume, has dealt with errors occuring in the output fiber of a neuron. This type of error is the same as that considered by Von Neumann (7), but Verbeek's attack on the problem of reliability yields different and highly interesting results. SECTION II: GENERALITY OF THE NEURON AS A COMPUTER COMPONENT Until now we have had to construct the neurons in any net we wished to make, for we have had no way of being certain that there does exist a neuron which will compute the desired logical functions for every step in threshold. We now show that for each Venn diagram containing excitation values, as in figure 4, there must always exist a neuron! In addition, we shall give an algorithm for the construction of a neuron from a Venn diagram, and investigate the problem of constructing neurons which are cheapest, in the sense that they receive a minimum number of fibers from the input. -2 A neuron will be constructed for the (=3)-Venn diagram of figure 10: This method of construction will then be extended to any & -Venn diagram, Let A be the sum of excitations to the neuron when the input configuration is ABC (in this case, A=1). Let AB be the sum of excitations to the neuron when |