By Dan Lawesson.

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A system description SD is a finite set of components. 2. A (global) system state is a mapping σ: SD → c∈SD S(c) such that σ(c) ∈ S(c) for all c ∈ SD. The set of all system states of a system description SD is denoted S(SD) . The state σ such that σ(c) = init(c) for all c ∈ SD is called the initial global state (denoted init(SD)). 3. e. we do not support dynamic creation or deletion of components. It is possible to simulate any bounded behavior of creation and deletion of components by introducing an initial state that corresponds to a component not yet being created and a final state that corresponds to the component being deleted, but unbounded creation of components is not supported.

1. 5, the diagram describes the behavior of a bus. , to! }, Σrec = { data? 1. Components To facilitate reasoning about events that have occurred among sets of interacting components we will instrument modeling component states with a history element which records important events before reaching the current state; namely events from Σlog ∪ Σcrit . 2. Let o = (Σ, Q, →, q0 ) be a modeling component. e. e | e ∈ Σ }. 3. 4. A memory component is a tuple c = (Σ, S, →, s0 , id) where • Σ is a finite set of events, • S is a finite set of extended component states, • → ⊆ S × Σ × S is a set of transitions, • s0 ∈ S is the initial state and • id is a function defined for all transitions of →.

Liveness can be expressed in the following way. In all paths of execution, Good should hold infinitely often. This means that at time of the execution, there is a future Good state, and it can be checked by the following CTL formula. AG(AF (Good)) In words, it is true for all states (AG), that eventually (AF ) Good will hold. This excludes any infinite computation not containing Good states. 2. Model Checking Mathematical Foundation 23 Chapter 3 Mathematical Foundation It’s 106 miles to Chicago, we’ve got a full tank of gas, half a pack of cigarettes, it’s dark and we’re wearing sunglasses.