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P
:=(
I; O; S; f
:
I
S
! (
S
;O
))
I = f1
;:::;
1g
O
= f
o
g
;n
2I
We also de
ne
I
as the set of all possible input sequences (the Kleene closure of
I
)
applying
I
If a modi
ed form of
P
program
P
y
with functionality
f
y
, where
f
6=
f
an internal state
s
y
and/or output sequence
O
that di
ers from those of
P
y
which normally operates on a subset
D
of all the possible inputs (
D
I
di
erences between
H
and
H
signal an unanticipated application of
P
We consider the
program state
of the computer at a point in execution to include all of the
State information is presented as a
nite set f
p
g where each
p
The use of
unde
ned
means that at some point in the execution of the program the value
program state domain
, D, is constructed by taking all possible values of each componentofthe
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