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This document explores key properties of a process defined in the context of Process Algebra, focusing on actions, transitions, and safety constraints. It examines the finite states of the process and delineates the conditions under which safety is preserved, such as the modifications to the program counter in response to actions. Moreover, it discusses the implications of parallel composition on safety and progress properties, with specific attention to fairness assumptions. The interplay between current and next states is analyzed to ensure that the process maintains integrity under various operational scenarios.
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In terms of Process Algebra Process P: 4 m a 1 2 5 m a box P var -- program counter action a :: {1,2} := +1 action b :: =3 :=1 method m :: ... b m 3
Properties Process P: 4 m a 1 2 5 m a m 3 Safety : constraints relating current and next state, e.g. = 1 unless = 2 {4,5} unless false Progress, e.g. = 1 {4,5}
x x [] 2 Parallel Composition 4 m a 1 2 5 m a m 3
x Properties under Parallel Composition 4 m a 1 2 5 m a m 3 These safety are preserved: = 1 unless = 2 {4,5} unless false Progress: = 1 {4,5} destroyed!
Preserved if we assume strong fairness. Properties under Parallel Composition 4 m a 1 2 5 m m 3 Progress: = 1 {4,5} Preserved if we assume weak fairness.
