Hardware Reference
In-Depth Information
I
V
Z
1
A
1
j
A
j
...
A
pj
Z
p
Fig. 12.4
A network topology to illustrate systems of equations
12.2.2
Windowing Via Solving a System of Equations
Given the composition
M
A
1
M
A
j
M
A
k
, consider a component FSM
M
A
j
and all component FSMs
M
A
1j
;:::;M
A
pj
with inputs that are connected with
the same output
M
A
j
,asinFig.
12.4
.
In this case, for each equation
V
of the FSM
M
X
M
A
1j
Š M
A
j
M
A
1j
;:::;M
X
M
A
pj
Š M
A
j
M
A
pj
, the input and output sets of their specifications
M
A
j
M
A
1j
;:::;M
A
j
M
A
pj
are respectively
.I;V;Z
1
/
,
:::
,
.I;V;Z
p
/
and contain those of the component
M
A
j
. Therefore, the output response of each solution (replacing
M
A
j
) to each input sequence coincides with that of the initial FSM
that are
.I; V /
M
A
j
because the
signal
must be produced as an external output, i.e., the solution of each equation
is equivalent to
V
M
A
j
cannot be optimized by
solving a single local equation. In order to be able to optimize such component we
need to hide some input or output alphabets of the component, i.e., to consider them
as internal alphabets. The latter can be achieved if we consider a system of equations
instead of a single equation.
The difference between a set of equations and a system of equations is that in the
former case a solution of any equation is a solution of the set of equations, whereas
in the latter case a solution of the system must be a solution of each equation of the
system. The definition of a system of FSM equations follows [151, 153].
M
A
j
, and therefore the component
Definition 12.2.1.
Given FSMs
M
A
1
; :::;M
A
k
and
M
C
1
; :::;M
C
k
,a
system of
FSM equations
8
<
M
X
M
A
1
Š M
C
1
M
X
M
A
2
Š M
C
2
:::
M
X
M
A
n
Š M
C
n
:
Search WWH ::
Custom Search