ComputerAided_Design_Engineering_amp_Manufactur.pdf
ComputerAided_Design_Engineering_amp_Manufactur.pdf
ComputerAided_Design_Engineering_amp_Manufactur.pdf
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n g<br />
n j<br />
Definition: The and of a TT (PP, TP, and PT) generation are transition (place, transition, place)<br />
and transition (place, place, and transition), respectively.<br />
For factor 2, ng and nj can be in the same or different PSPs. For the latter case, there are five possibilities:<br />
(1) sequential earlier (SE), (2) sequential later (SL), (3) concurrent (CN), (4) exclusive (EX), and (5) cyclic (CL).<br />
Definition: Let �g ( �j) denote the PSP that contains the generation point (joint). Pure generation (PG)<br />
generates paths within a single PSP (Figure 8.2), i.e., �g � �j . Interactive generation (IG) generates<br />
paths between two PSPs (Figure 8.4), i.e., �g ��j .<br />
Definition: If ng → nj prior to the generation, then it is a forward generation; otherwise it is a backward<br />
generation.<br />
In Figure 8.2, [t1 p4 t3] is a forward generation; �6 in Figure 8.4(a) is a backward generation. A<br />
backward TT generation needs the addition of tokens to the NP to avoid the resulting N being nonlive.<br />
This constitutes Rule TT.2.<br />
The idea of constructing the rules is simple. An eligible generation upon N to produce should<br />
not alter the marking and firing behavior of . Furthermore, the new PSP must be live and bounded.<br />
One of the following three actions is taken depending on the type of generation: (1) forbidden,<br />
(2) permitted, or (3) permitted but need more generations. For instance, a TP generation causes<br />
an extra token to be injected into the original net whenever the NP gets a token. This alters the<br />
marking behavior of and the net is unbounded. A PT generation robs a token from and<br />
causes to be nonlive, hence changing its firing behavior. To avoid this problem, add more<br />
generations or forbid such generations. The rules are complete in the sense that all possible generations<br />
have been considered.<br />
The following definitions for TT and PP rules have considered all possible structural relationships<br />
between and . Some generations are forbidden, some require the addition of tokens, while others<br />
require further generations.<br />
1<br />
N 2<br />
N 1<br />
N 1<br />
N 1<br />
N 1<br />
N 1<br />
ng nj Definition: TT Rule:<br />
For an NP from tg � �g to tg � �j generated by the designer,<br />
(0) TT.0 If tg � tj or only one of them is in a cycle, which was solely generated using Rule PP.1, then<br />
signal “forbidden, delete the � ” and return.<br />
(1) TT.1 If � , signal “a pure TT generation;” otherwise signal “an interactive TT generation.”<br />
(2) TT.2 If ← , signal “forming a new cycle.”<br />
If, without firing , there does not exist a firing sequence � to fire , then insert token in a<br />
place of NP.<br />
If � , return and the designer may start a new generation.<br />
(3) TT.3 If the structure synchronic distance � � then<br />
(a) TT.3.1<br />
Apply Rule TT.4.<br />
(b) TT.3.2<br />
Generate a new TT-path path to synchronic and such that after step 3.c,<br />
changes from � to 1.<br />
(c) TT.3.3<br />
Go to step 2.<br />
(4) TT.4<br />
(a) TT.4.1<br />
Generate a TP-path from a transition of each in to a place in the NP.<br />
(b) TT.4.2<br />
Generate a virtual PSP, a PT-path, from the place to a transition of each in .<br />
w<br />
�g �j tg tj tj tg �g �j s<br />
dgj s<br />
tg tj dgj tg �g Xgj pk n˙ j tj �j Xjg Definition: PP Rule:<br />
For an NP from pg � �g to pj � �j generated by the designer,