The authors previously give a type system that guarantees that well-typed multi-threaded programs are possibilistically noninterfering. If thread scheduling is probabilistic, however, then well-typed programs may have probabilistic timing channels. They describe how they can be eliminated without making the type system more restrictive. They show that well-typed concurrent programs are probabilistically noninterfering if every total command with a high guard executes atomically. The proof uses the concept of a probabilistic state of a computation, following the work of Kozen (1981).
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