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Identity

The identity relation for a given language *L* is
. For a given pfsr
, the identity relation is given by the pfst
.
Note that it would be wrong to define
. Suppose is true only of
. The pair then would be true of the
pairs of symbols
, whereas identity requires that we only allow
the pairs
. Another
example to stress the point: the expression `
identity(?)` (`copy') is quite different from ` ?:?` (`garbage-in
garbage-out').
It is therefore necessary to introduce an identity marker for each of
the transitions. The identity of a pfsr
is
given by
where
.
The operations * domain*, * range* and * inverse* are
straightforward. For a given pfst
,
we have:

*Noord G.J.M. van*

*2001-06-22*