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ComputerAided_Design_Engineering_amp_Manufactur.pdf

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q u<br />

: the numerator of the least ratio<br />

R or R (N, M0): reachable set of markings of N with initial marking M0 R : least firing ratio<br />

: least firing-marking ratio<br />

: least marking ratio<br />

: least marking-firing ratio<br />

SC: synchronized choice nets<br />

SPN: Stochastic PNs<br />

t: transition<br />

: a control transition<br />

•t (t•): the set of input (output) places of transition p<br />

: the (prime) start transition for a pair of concurrent PSPs<br />

T: the set of transitions in net N<br />

T-Matrix: temporal matrix<br />

TP-path: transition-place path<br />

TT generation: transition-transition path generation<br />

SE or E (→): sequentially earlier<br />

SL or L (←): sequentially later<br />

SN or N (←): sequentially next<br />

SP or P (←): sequentially previous<br />

SQ: sequential<br />

subscript g : related to generation point<br />

subscript j : related to joint<br />

superscript 1: for the net prior to the generation, i.e., refers to the net (T, P, M, and<br />

R) prior to the generation<br />

superscript 1a: for the net prior to the generation and every home place has only one token, i.e.,<br />

superscript 2: for the net after the generation, i.e., refers to the net (T, P, M, and R)<br />

after the generation<br />

superscript w: for the NP, i.e., refers to the (T, P, M) of the NP. denotes a complete<br />

firing sequence through the NP, which includes both and .<br />

�: transition firing sequence<br />

� (t): the number of firings of t in �<br />

VP: virtual PSP which has only the generation point and the joint<br />

X: local exclusive set<br />

: LEX<br />

: literally greater than<br />

�: a circuit<br />

� : a handle<br />

f<br />

R fm<br />

R m<br />

R mf<br />

tc ts( tps) N 1 T 1 , P 1 , M 1 , R 1<br />

( )<br />

N 1a<br />

T 1a , P 1a , M 1a R 1a<br />

( )<br />

N 2 T 2 , P 2 , M 2 , R 2<br />

( )<br />

T w , P w , M w<br />

( ) � w<br />

ng nj Xik ( �i, �k) �lit

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