ComputerAided_Design_Engineering_amp_Manufactur.pdf

FIGURE 8.1 A basic process. (From Reference 2a. With permission.)
Definition: Let ta � T be enabled in M0, �ph�•t a, ph is a home place. The set of home places is denoted
as H � {ph ph is a home place}.
Home places actually form the home states of the synthesized net.
Definition: A pseudoprocess (PSP) in a PN is a DEP [ n1n 2…n k]
, k � 2 such that
|•ni| � |ni•| � 1, 2� i� k�1 , or
k � 2. The PSP is termed a virtual PSP (VP).
ng( nj) � n1( nk) is defined as the generation point (joint). n is defined as the
next generation point (next joint).
Figure 8.1 shows a basic process with p1 as a home place. In Figure 8.2(3), [t1 p2 t2 p3 t3] ([p1 t1
p2]) is a PSP whose and nj = t3 (p2), respectively. Note the VP in Figure 8.3 contains
only and . and are also used in new-path generations.
Definition: Let NP be a set of new paths generated from a set of nodes called generation points
in to another set of nodes called joints in to produce is a node
.
A PN consists of a number of PSPs; each is considered a process. This may save the time involved in
the synthesis compared with that which considers each individual node. When we generate a new PSP
from to we generate a new process or a new PSP. Mutual relationships among processes may be
sequential, concurrent, or exclusive as will be defined below.
Definition: If in a PN are in the same elementary cycle, then
• i.e., they are sequential (SQ) to each other, if the cycle has tokens, if the DEP from
to is an A-path, then i.e., is sequential earlier (SE) than otherwise
i.e., is sequential later (SL) than . A special case of “SE” (“SL”) is “SP” (“SN”)
if the of equals of .
• otherwise, if the cycle contains no tokens, then i.e., they are cyclic (CL) to each other.
Definition: Let DEP1� and DEP2 � , where DEP1 � DEP2� ,
and are two PSPs, and there are no DEPs (called bridges) from a node DEP1 to a node
˙g n˙ ( j)
� n2( nk � 1)
ng � t1( p1)
( �1) ng nj ng nj n˙ , , g nj ( ng) N 1
( nj) N 1
N 2 n˙ g n˙ � ( j)
nk � NP
and nk � ng•( •nj) ng ne, �1 and �2 �1 ↔ �2, �1 �2 �1 → �2; �1 �2; �1 ← �2; �1 �2 nj ( ng) �1 ng( nj) �2 �1o� 2;
[ npsn2…n k�1] [ npsn2�…n k�� 2]
{ nps} �1 �2 ( �nps) P1
t1
P2
t2
P3
t3