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Ln , s0n , sn )} be a partition, and let sk be the partition state. The initial partition state is s0 = s01 , . . s0n . We say that the partition P is consistent if there exists a sequence of operation instances L = α1 , . . , αk such that: 1. 2. 3. 4. 4 α ∈ Li ⇒ α ∈ L α α s0 1 . . k sk Every sj ∈ {s0 , . . , sk } is constraint consistent αi → αj ⇒ i < j Application-Middleware Dependencies In Sect. 3 we introduced integrity constraints and an order relation between operations. These concepts are used to ensure that the execution of operations is performed according to the clients’ expectations.

Nadjm-Tehrani we do not explicitly model. First, in order to prove that the reconciliation phase ends with the installment of a consistent partition state, we need to assume that the state from which the reconciliation started is consistent. This is a reasonable assumption since normal and degraded mode operations always respect integrity constraints.

This event is also coherent with requirement SAF-2, which says that "the signal of a route can only be green when all blocks of that route are reserved for it and are unoccupied". This is due to invariant inv3_2 equating the blocks with green signal with ready routes, and invariants inv2_2 and inv2_3 telling that ready routes have all their blocks reserved and unoccupied. route_formation any r where r ∈ resrt \ f rm rsrtbl−1 [{r}] ✁ nxt(r) = rsrtbl−1 [{r}] ✁ T RK then f rm := f rm ∪ {r} GRN := GRN ∪ {SIG(f st(r))} end This logical event acts on the physical variable GRN .

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Computer. Fraud & Security (September 2005)
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