Hardware Reference
In-Depth Information
A
2
j
A
1
A
1
j
A
2
A
j
A
pj
A
3
j
Fig. 12.3
Local
optimization
of
FSM
M
A
j
with
respect
to
neighbour
FSMs
M
A
1j
;
M
A
2j
;:::;M
A
pj
equation
M
X
M
A
t
Š M
A
j
M
A
t
, the composition
M
A
1
M
B
j
M
A
n
where
M
B
j
replaces the component FSM
M
A
j
, is equivalent to the composition
M
A
1
M
A
j
M
A
n
.
Proposition
12.2.1
can be used to define heuristics that simplify the problem
of resynthesis and optimization of a component FSM, at the price of a loss of
completeness and optimality. As an example, consider the topology shown in
Fig.
12.3
, in order to resynthesize the FSM
M
A
j
we may take the collection
M
A
1j
; :::;M
A
pj
of all FSMs connected with FSM
M
A
j
andthenderivethe
collection of equations:
M
X
1
M
A
1j
Š M
A
j
M
A
1j
;
:::
M
X
P
M
A
pj
Š M
A
j
M
A
pj
:
Replacements for
M
A
j
are to be found among the reductions of each of the previous
equations; to guarantee that a given reduction is a solution we can apply sufficient
conditions, e.g., replacing a Moore FSM only by Moore reductions of the largest
solution. An optimal solution is selected from the solutions over all equations, i.e.,
we solve each equation, select an optimal solution of the equation and then select
the best solution over all optimal solutions.
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