PrÃklady
PrÃklady
PrÃklady
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RNDr. Peter Kaprálik, PhD.<br />
Príklady z Logických systémov<br />
1 E 2 3, 3 E 2 5, 5 E 2 6 2E 2 4, 4 E 2 9,<br />
7E 2 8<br />
1 E 2 5, 3 E 2 6, 2 E 2 9,<br />
1 E 2 6,<br />
(1, a) = 1, (3, a) = 7, 1 E/ 1 7 e 1 E/ 2 3,<br />
(1, a) = 1, (5, a) = 8, 1 E/ 1 8 e 1 E/ 2 5,<br />
(1, a) = 1, (6, a) = 7, 1 E/ 1 7 e 1 E/ 2 7,<br />
(3, a) = 7, (5, a) = 8, 7 E 1 8, (3, b) = 9, (5, b) = 4, 9 E 1 4, e 3 E 2 5,<br />
(3, a) = 7, (6, a) = 7, 7 E 1 7, (3, b) = 9, (6, b) = 4, 9 E 1 4, e 3 E 2 6<br />
5 E 2 3, 3 E 2 6 e 5 E 2 6,<br />
Ďalej uvádzame už len výsledky:<br />
2 E/ 2 4, 2 E/ 2 9, 4 E 2 9, 7 E 2 8.<br />
Teda<br />
E 2 = 1 , 3, 5, 6 , 2 , 4, 9 , 7, 8<br />
Teraz zisťujeme či platí: 3 E 3 5, 3 E 3 6, 5 E 3 6, 4 E 3 9, 7 E 3 8.<br />
(3, a) = 7, (5, a) = 8, 7 E 2 8, (3, b) = 9, (5, b) = 4, 9 E 2 4, e 3 E 3 5,<br />
(3, a) = 7, (6, a) = 7, 7 E 2 7, (3, b) = 9, (6, b) = 4, 9 E 2 4, e 3 E 3 6,<br />
5 E 3 3, 3 E 3 6 e 5 E 3 6,<br />
(4, a) = 3, (9, a) = 3, 3 E 2 3, (4, b) = 3, (9, b) = 6, 3 E 2 6, e 4 E 3 9,<br />
(7, a) = 3, (8, a) = 6, 3 E 2 6, (7, b) = 4, (8, b) = 9, 4 E 2 9, e 7 E 3 8.<br />
E 3 = E 2 = E = 1 , 3, 5, 6 , 2 , 4, 9 , 7, 8<br />
R<br />
Označme s 1 = 1 , s 2 = 3, 5, 6 , s 3 = 2 , s 4 = 4, 9 , s 5 = 7, 8 . Potom redukovaný<br />
automat A je daný tabuľkou<br />
a b<br />
s 1 s 1 /0 s 3 /0<br />
s 2 s 5 /0 s 4 /0<br />
s 3 s 4 /1 s 4 /0<br />
s 4 s 2 /1 s 2 /0<br />
s 5 s 2 /1 /1<br />
s 4<br />
.<br />
.<br />
Príklad 3. Nájdite ekvivalentné stavy medzi automatmi<br />
ekvivalentné<br />
A, B. Sú tieto automaty<br />
A a b<br />
B a b<br />
s 1 s 2 /0 s 3 /1<br />
t 1 t 3 /1 t 2 /0<br />
s 2 s 1 /1 s 3 /0<br />
t 2 t 1 /0 t 2 /1<br />
s 3 s 2 /0 s 1 /1<br />
t 3 t 1 /1 t 2 /0<br />
s 4 s 4 /0 s 1 /1<br />
Riešenie. Vytvoríme nový automat A 4 B - zjednotenie automatov A, B a v ňom nájdeme<br />
ekvivalentné stavy.<br />
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