10.01.2013 Views

ComputerAided_Design_Engineering_amp_Manufactur.pdf

ComputerAided_Design_Engineering_amp_Manufactur.pdf

ComputerAided_Design_Engineering_amp_Manufactur.pdf

SHOW MORE
SHOW LESS

Create successful ePaper yourself

Turn your PDF publications into a flip-book with our unique Google optimized e-Paper software.

DSP: digital signal processing<br />

EFC: extended free-choice nets<br />

EX (|): exclusive<br />

FC: free-choice nets<br />

G (J): the set of �g ( �j) involved in a single application of the TT or PP rule<br />

GPN: general Petri nets<br />

H: the set of home places<br />

Hc : the least amount of tokens required in home place pbh for the synthesized net to be live<br />

I: an input function defining the set of directed arcs from P to T<br />

IG: interactive generation<br />

L: language of Petri net<br />

LCN: local concurrent set of PSPs<br />

LEX: local exclusive set of PSPs<br />

M: marking<br />

M or : the marking of in<br />

N: a PN<br />

: a synthesized PN with every home place holding only one token<br />

: a PN after adding tokens to<br />

: an and<br />

: an and<br />

: the subnet in<br />

n: the number of PSPs in a Petri net<br />

ni: the number of PSPs before the ith generation<br />

: the (next) generation point<br />

: the (next) joint<br />

: the prime start node (place, transition)<br />

NP: new path<br />

O: an output function defining the set of directed arcs from T to P<br />

OPN: ordinary Petri nets<br />

p: place<br />

: a home place in the basic process<br />

: a decision place<br />

: the set of input (output) transitions of place p<br />

: the (prime) start place for a pair of exclusive PSPs<br />

: a prime start place relative to and<br />

P: the set of places in net N<br />

: directed path<br />

PG: pure generation<br />

�: process<br />

�: PSP<br />

: the PSP containing<br />

: the PSP containing<br />

: new PSP<br />

PN: Petri net<br />

PP generation: place-place path generation<br />

PP-path: place-place path<br />

PT-Path: place-transition path<br />

PSP: pseudo-process<br />

q: least ratio<br />

[q]’: the fraction , where q is any ratio, and a� and b� are relatively prime<br />

: the denominator of the least ratio<br />

2 N 1<br />

( ) M 1�2<br />

N 1<br />

N 2<br />

N a<br />

N b<br />

N a<br />

N 1a<br />

N 1<br />

N a<br />

N 2a<br />

N 2<br />

N a<br />

N 1�2<br />

N 1<br />

N 2<br />

ng n˙ ( g)<br />

nj n˙ ( j)<br />

nps( pps, tps) pbh pd •p( p•)<br />

ps( pps) gj<br />

pps ng nj P<br />

�g ng �j nj � w<br />

a�<br />

a-----<br />

b�<br />

b<br />

q 1

Hooray! Your file is uploaded and ready to be published.

Saved successfully!

Ooh no, something went wrong!