292 



Information Storage and Neural Control 



exerts +2 excitation on the third. Then its threshold can vary 

 harmlessly: 3 < < 6, or nearly 50 per cent. Moreover, if the 

 threshold is better controlled, then the strength of the signals can 

 vary. Finally, if both are fairly well controlled, the connections 

 can be wrong, as in Figure 7(c), and the input-output function 

 [S5] is still undisturbed. 



If we want to extend our symbols to four arguments, then the 

 pattern becomes that of Figure 8, and for five arguments it becomes 

 more complex. In general, each new line must divide all existing 

 areas into two; thus for N inputs there are 2 spaces. Oliver Selfridge 

 and Marvin Minsky have worked out simple ways of making such 

 symbols, with sine waves, for any finite number of inputs. 



Eugene Prange has invented a way of devising the distribution 

 of don't-care conditions so that there are as many as possible for 

 a net of N neurons in the first rank and one in the output rank, 

 each rank having N inputs per neuron. The number of don't-care 

 conditions, or dashes, depends upon the number of ones in the 

 spaces for the function to be computed. The dashes are fewest 

 when the function to be coinputed has exactly one-half its spaces 

 filled with ones. Manuel Blum has solved the following questions: 

 1) Suppose that there are no don't-care conditions, or dashes, in 

 the symbol for the output neuron; what fraction of the spaces for 

 each neuron of the first rank can have dashes and the calculation 

 be error-free for the toughest function (half-filled with ones), all 

 as a function of N?; 2) With all those dashes in the first rank, what 



1.0 



0.5 



Figure 8 



50 



Figure 9 



100 



