TRANSMISSION OF VARIETY 8/7 



8/7. Designing an inverter. The previous section showed that, 

 provided the transducer did not lose distinctions in transmission 

 from input to output, the coded message given as output could 

 always be decoded. In this section we shall show that the same 

 process can be done automatically, i.e. given a machine that does not 

 lose distinctions, it is always possible to build another machine that, 

 receiving the first's output as input, will emit the original message 

 as its own output. 



We are now adopting a rather different point of view from that 

 of the previous section. There we were interested in the possibility 

 of a message being decoded and in whether the decoding could be 

 done or not — by whom did not matter. We are now turning to the 

 question of how a mechanism can be built, by us, so that the mechan- 

 ism shall do the decoding automatically. We seek, not a restored 

 message but a machine. How shall it be built ? What we require 

 for its specification, of course, is the usual set of transformations 

 (S.4/1). 



A possible method, the one to be used here, is simply to convert 

 the process we followed in the preceding section into mechanistic 

 form, using the fact that each transition gives information about the 

 parameter-value under which it occurred. We want a machine, 

 therefore, that will accept a transition as input and give the original 

 parameter value as output. Now to know which transition has 

 occurred, i.e. what are the values of / and j in "l',-^ X/\ is clearly 

 equivalent to knowing what is the value of the vector (i,j); for a 

 transition can also be thought of as a vector having two components. 

 We can therefore feed the transitions into an inverter if the inverter 

 has an input of two parameters, one to take the value of the earlier 

 state and the other to take the value of the later. 



Only one difficulty remains : the transition involves two states that 

 do not exist at the same moment of time, so one of the inverter's 

 inputs must behave now according to what the transducer's output 

 was. A simple device, however, will get over this difficulty. 

 Consider the transducer 



Suppose it is started at state /• and is given the input Q S S RQ S 

 R R Q; its output will be rqssrqsrr q, i.e. after the first letter 

 it just repeats the input, but one step later. Two such transducers 



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