Observational determinism has been proposed in the literature as a way to ensure confidentiality for multi-threaded programs. Intuitively, a program is observationally deterministic if the behavior of the public variables is deterministic, i.e., independent of the private variables and the scheduling policy. Several formal definitions of observational determinism exist, but all of them have shortcomings; for example they accept insecure programs or they reject too many innocuous programs. Besides, the role of schedulers was ignored in all the proposed definitions. A program that is secure under one kind of scheduler might not be secure when executed with a different scheduler. The existing definitions do not always ensure that an accepted program behaves securely under the scheduler that is used to execute the program. Therefore, this paper proposes a new formalization of scheduler-specific observational determinism. It accepts programs that are secure when executed under a specific scheduler. Moreover, it is less restrictive on harmless programs under a particular scheduling policy. We discuss the properties of our definition and argue why it better approximates the intuitive understanding of observational determinism. In addition, we also discuss how compliance with our definition can be verified, using model-checking.
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