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SEKE 2012 Proceedings - Knowledge Systems Institute

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Fig. 3. Example a 3-compound weakly dependent siphon. S 0 =S 6 =S 1 ⊕S 2 ⊕S 3 , S 4 =S 1,2 , S 5 =S 2,3 and η 0 =η 1 +η 2 +η 3 -η 4 -η 5 .<br />

TABLE III<br />

EIGHT SMS S, AND CORE CIRCUITS IN FIG. 3.<br />

S Set of places c<br />

S 1 p 5 , p 17 , p 14 , p 15 , p 16 c 1 =[p 14 t 4 p 16 t 1 p 15 t 2 p 14 ]<br />

S 2 p 4 , p 26 , p 12 , p 13 , p 14 , p 15 c 2 =[p 15 t 2 p 14 t 3 p 13 t 18 p 12 t 8 p 15 ]<br />

S 3 p 2 , p 27 , p 11 , p 12 , p 13 c 3 =[p 13 t 18 p 12 t 17 p 17 t 14 p 13 ]<br />

S 4 p 4 , p 17 , p 14 , p 15 c 4 =[p 15 t 2 p 14 t 6 p 15 ]].<br />

S 5 p 2 , p 26 , p 12 , p 13 c 5 =[p 13 t 18 p 12 t 12 p 13 ]<br />

S 6 p , p , p , p , p , p , p , p 16 5 27 11 12 13 14 15 c 6 =c 1 ⊕c 2 ⊕c 3<br />

S 7 p 5 , p 26 , p 12 , p 13 , p 14 , p 15 , p 16 c 7 = c 1 ⊕c 2<br />

S 8 p 4 , p 27 , p 11 , p 12 , p 13 , p 14 , p 15 c 8 = c 2 ⊕c 3<br />

TABLE IV<br />

EIGHT SMS S,[S] AND η IN FIG. 3.<br />

S Set of places [S] η<br />

S 1 p 5 , p 17 , p 14 , p 15 , p 16 p 3 , p 4 , p 7 , p 8 , p 9 , p 10 t 1 -t 3 +t 7 -t 10<br />

S 2 p 4 , p 26 , p 12 , p 13 , p 14 , p 15 p 2 , p 3 , p 8 , p 9 , p 10 , p 17 , p 21 , p 23 , p 24 , p 25 t 2 -t 4 +t 13 -t 17<br />

S 3 p 2 , p 27 , p 11 , p 12 , p 13 p 20 , p 21 , p 23 , p 24 , p 25 , p 26 -t 8 +t 14 -t 16 +t 18<br />

S 4 p 4 , p 17 , p 14 , p 15 p 3 , p 8 , p 9 , p 10 t 2 -t 3 -t 4 +t 7<br />

S 5 p 2 , p 26 , p 12 , p 13 p 21 , p 23 , p 24 , p 25 -t 8 +t 13 -t 17 +t 18<br />

S 6 p 5 , p 27 , p 11 , p 12 , p 13 , p 14 , p 15 , p 16 p 2 , p 3 , p 4 , p 7 , p 8 , p 9 , p 10 , p 17 , p 20 , p 21 , p 23 , p 24 , p 25 , p 26 t 1 -t 10 +t 14 -t 16<br />

S 7 p 5 , p 26 , p 12 , p 13 , p 14 , p 15 , p 16 p 2 , p 3 , p 4 , p 7 , p 8 , p 9 , p 10 , p 17 , p 21 , p 23 , p 24 , p 25 t 1 -t 10 +t 13 -t 17<br />

S 8 p 4 , p 27 , p 11 , p 12 , p 13 , p 14 , p 15 p 2 , p 3 , p 8 , p 9 , p 10 , p 17 , p 20 , p 21 , p 23 , p 24 , p 25 , p 26 t 2 -t 4 +t 14 -t 16<br />

362

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