Abstract
We study the complexity of the Shortest Linear Program (SLP) problem, which is to minimize the number of linear operations necessary to compute a set of linear forms. SLP is shown to be NP-hard. Furthermore, a special case of the corresponding decision problem is shown to be Max SNP-Complete.
Algorithms producing cancellation-free straight-line programs, those in which there is never any cancellation of variables in GF(2), have been proposed for circuit minimization for various cryptographic applications. We show that such algorithms have approximation ratios of at least 3/2 and therefore cannot be expected to yield optimal solutions to non-trivial inputs.
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Boyar, J., Matthews, P., Peralta, R. (2008). On the Shortest Linear Straight-Line Program for Computing Linear Forms. In: Ochmański, E., Tyszkiewicz, J. (eds) Mathematical Foundations of Computer Science 2008. MFCS 2008. Lecture Notes in Computer Science, vol 5162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85238-4_13
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DOI: https://doi.org/10.1007/978-3-540-85238-4_13
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