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V
=
f
FB
;
N
;
ZN
;
m.ZN
g
=(FB=
?^
N=
?^
ZN =
?^
m.ZN = 1)
8
:
9
;
N
0
= f FB
0
6
FB
0
ZN
0
−
=
?
then
else
1
m.ZN
0
= f N
0
6
N
0
^
=
?
then
else
m.ZN
a
=
ZN
0
= f N
0
6
^
=
?
then
m.ZN else
?
ZN
0
FB
0
^
1
,
=
?
In the following sections, we assume that the type denitions for variables also
specify the \
type" of variables, i.e. whether they are input, output,
register, memorization or local variables. The respective sets of variables are
denoted by
Signal
I;O;R;M;L
. Combinations of these letters stand for the union of the
respective sets; e.g.
stands for the set of input/output/register variables of
some system. Note that the
IOR
M
variables are not originally present in the
Signal
program, but are introduced by its translation into the
notation.
For the translation validation process, the generated C programs is also trans-
lated into the sts formalism. Below, we present the sts representation of the
DEC
iterate() generated code, where the predicate
pres-but
(
sts
U
) indicates that all
V n U
variables in the set
preserve their values during the respective transition.
Thus, the values of all variables except, possibly, those in
U
are preserved.
C
=(
V
c
;
c
;
c
)where
V
=
f
FB
c
;
N
c
;
ZN
c
;
h1
c
;
h2
c
g
=(ZN
c
=1
^
pc
=
l
0
)
8
:
9
;
h1
0
c
=
pc
0
=
(
pc
=
l
0
^
T
^
l
1
^
pres-but
(pc
;
h1
c
))
h2
0
c
=(ZN
c
pc
0
=
_
(
pc
=
l
1
^
1)
^
l
2
^
pres-but
(pc
;
h2
c
))
pc
0
=
_
(
pc
=
l
2
^
h2
c
^
l
2
:
1
^
pres-but
(pc))
pc
0
=
_
(
pc
=
l
2
^:
h2
c
^
l
3
^
pres-but
(pc))
pc
0
=
_
(
pc
=
l
2
:
1
^
l
3
^
pres-but
(pc
;
FB
c
))
pc
0
=
c
=
_
(
pc
=
l
3
^
h2
c
^
l
3
:
1
^
pres-but
(pc))
_
l
3
pc
0
=
(
pc
=
^:
h2
c
^
l
3
:
2
^
pres-but
(pc))
N
0
c
=FB
c
pc
0
=
_
(
pc
=
l
3
:
1
^
^
l
4
^
pres-but
(pc
;
N
c
))
N
0
c
=ZN
c
−
_
l
3
:
2
^
^
pc
0
=
l
4
^
;
(
pc
=
1
pres-but
(pc
N
c
))
_
(
pc
=
l
4
^
pc
0
=
l
5
^
pres-but
(pc))
ZN
0
c
=N
c
pc
0
=
_
(
pc
=
l
5
^
^
l
0
^
pres-but
(pc
;
ZN
c
))
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