By Arora S., Karakostas G.
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In this way, in each configuration, Mr knows the symbol seen by each of the heads of M, and is able to simulate it by a transition function that correctly updates the new contents of the tape and all the new components of the state. It just remains to add to Mr a "preprocessing" to compress the input, translating it into the new alphabet. This can be done by writing down a symbol upon reading each r consecutive symbols of the input, which requires no additional space. The construction of the transition table of Mr from that of M is straightforward.
When it must be clear that a machine is not a transducer, sometimes the name acceptor is used. If the machine is a transducer, the function it computes is defined on its accepted language, and for each accepted input the value of the function is the word which appears in the output tape when the machine stops in an accepting state. The concepts of configuration and computation for transducers are defined exactly as for acceptors. The description of the output tape is included in the configuration.
Observe that allowing a constant number of "next move" possibilities greater than two is in some sense useless. An election among k possibilities can be substituted by log k elections among two possibilities. If k is a constant, then the computation is only a constant factor longer. Thus, we lose no generality Models of Computation: Nondeterministic Turing Machines 27 if we require in our model that for every pair (q, a), 16(q, a)1 ~ 2. This fact is usually expressed by saying that the machines have "nondeterministic fan-out 2".