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The newly emerging many-core-on-a-chip designs have renewed an intense interest in parallel processing. By applying Amdahlpsilas formulation to the programs in the PARSEC and SPLASH-2 benchmark suites, we find that most applications may not have enough parallelism for modern parallel machines. However, value prediction techniques may allow the ldquoparallelizationrdquo of the sequential portion by predicting values before they are produced. We here extend Amdahlpsilas formulation to model the data redundancy inherent to each benchmark. Our analysis shows that the performance of PARSEC suite benchmarks may improve by a factor of 180.6% and 232.6% for the SPLASH-2 suite, compared to when only the intrinsic parallelism is considered. This demonstrates the immense potential of fine-grained value prediction in enhancing the performance of modern parallel machines.