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Hardware Trust is an emerging problem in semiconductor integrated circuit (IC) security due to widespread outsourcing and the stealthy nature of hardware Trojans. Conventional post-manufacturing testing, test generation algorithms and test coverage metrics cannot be readily extended to hardware Trojan detection. As a result there is a need to develop approaches that will ensure trusted in-field operation of ICs, and more generally trust in computing. We present a distributed software scheduling prototype, TADS (Trojan Aware Distributed Scheduling), to achieve a Trojan-activation tolerant trustworthy computing system in a multi-core processor potentially containing hardware Trojans. TADS is designed to be transparent to applications and can run on general purpose multicore PEs without modifications to the operating system or underlying hardware. TADS can, with high confidence, continue to correctly execute its specified queue of job subtasks in the presence of hardware Trojans in the multi-core PEs while learning the individual trustworthiness of the individual PEs. Specially crafted self-checking subtasks called bounty hunters are introduced to accelerate PE trust learning. Also, by learning and maintaining individual PE trustworthiness, the scheduler is able to achieve Trojan containment by scheduling subsequent job subtasks to PEs with high learned trust.