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Fast Forward Permutations
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Title: Fast Forward Permutations Research Question: Can we create a permutation that allows for efficient computation of its values, even when given only a few calls to an underlying permutation? Methodology: The researchers proposed a new method called the "Choose Cycle Lengths" (CCL) process. This process generates a sequence of numbers that represents the lengths of the cycles in a permutation. They then used this process to create a new type of permutation called a "fast forward permutation." This permutation is designed to have its values computed efficiently, even when given only a few calls to the underlying permutation. Results: The researchers proved that their CCL process generates a sequence of numbers that represents the lengths of the cycles in a permutation, and that this sequence can be used to create a fast forward permutation. They also showed that the expected running time of their CCL process is O(log|Ω|), making it highly efficient. Implications: The creation of fast forward permutations has several implications. First, it solves an open problem in the field of computer science. Second, it provides a new method for creating permutations with efficient computation times, even when given only a few calls to an underlying permutation. This could have practical applications in various fields, such as cryptography and data processing. Link to Article: https://arxiv.org/abs/0112016v1 Authors: arXiv ID: 0112016v1 [[Category:Computer Science]] [[Category:Permutation]] [[Category:Process]] [[Category:This]] [[Category:Fast]] [[Category:Forward]]
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