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sav07_lecture_18 [2007/05/28 21:33] vasu.singh |
sav07_lecture_18 [2007/05/28 21:33] vasu.singh |
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This suggests that the two programs above are not equivalent for the purpose of reasoning | This suggests that the two programs above are not equivalent for the purpose of reasoning | ||
in concurrently executing programs. | in concurrently executing programs. | ||
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Let $A = \{bar, rab\}$ and $B = \{bara\}$. Then $A.B = \{barbara, rabbara\}$ and $A \cup B = \{bar, rab, bara\}$. | Let $A = \{bar, rab\}$ and $B = \{bara\}$. Then $A.B = \{barbara, rabbara\}$ and $A \cup B = \{bar, rab, bara\}$. | ||
- | $[[ C_1 || C_2 ]] = \bigcup {\{I(S_1,S_2)\}} where $S_1 = [[C_1]]$ and $S_2 = [[C_2]]$, where | + | $[[ C_1 || C_2 ]] = \bigcup {\{I(S_1,S_2)\}}$ where $S_1 = [[C_1]]$ and $S_2 = [[C_2]]$, where |
$I(S_1,S_2) = \{S_1^1, S_2^1, \ldots, S_1^n, S_2^n \mid S_1 = S_1^1 S_1^2 \ldots S_1^n$ and $S_2 = S_2^1 S_2^2 \ldots S_2^n \}$. | $I(S_1,S_2) = \{S_1^1, S_2^1, \ldots, S_1^n, S_2^n \mid S_1 = S_1^1 S_1^2 \ldots S_1^n$ and $S_2 = S_2^1 S_2^2 \ldots S_2^n \}$. |