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#### 4.11  Inverse Machine

An inverse machine Mi is a machine which is developed from the given machine M with its output sequence and produces the input sequence given to machine M, after at most a finite delay.

A deterministic inverse machine can be constructed if and only if the given machine is lossless. The machine can produce the input sequence applied to the original machine after at most a finite delay if and only if M is lossless of a finite order.

Consider the following example.

#### Example 4.22

Construct an inverse machine of the following given machine:

Solution:

Present State
Next State, z
X = 0
X = 1
A
B, 0
C, 1
B
C, 1
D, 0
C
A, 0
D, 1
D
A, 1
C, 0

We have to construct the inverse machine of this given machine.

Before constructing ...

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