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General Purpose GPU (GPGPU) computation relies heavily on intrinsic high data-parallelism to achieve significant speedups. However, application programs may not be able to fully utilize these parallel computing resources due to intrinsic data dependencies or complex data pointer operations. In this paper, we use aggressive software-based value prediction techniques on GPUs to accelerate programs that lack inherent data parallelism. This class of applications are typically difficult to map to parallel architectures due to data dependencies and complex data pointers present in the application. Our experimental results show that, despite the overhead incurred due to software speculation and the communication overhead between the CPU and GPU, we obtain up to 6.5x speedup on a selected set of kernels taken from the PARSEC and Sequoia benchmark suites.