(4) For an event expression ee1ee2, where ee1 and ee2 are two event expressions,

P( e e 1 e e 2 )=P( e e 1 )+P( e e 2 )*P( e e 2 ), P( e e 1 e e 2 ) P( e i ) ={ P( e e 1 ) P( e i ) *( 1P( e e 2 ) ), if e i occursine e 1 P( e e 1 ) P( e i ) *( 1P( e e 2 ) ), if e i occursine e 2 .( 12.8 )

Implementation Details. An event expression ee can be represented by a binary tree T where each leaf node denotes a basic event identifier and each non-leaf node denotes an operator ∧, ∨ or ∼. Figure 12.4 gives an example of a binary tree which represents the event expression (e1∧ ∼e2) ∨ (e3∧ ∼e4) ∨ (e5∧ ∼e6).

For each node

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