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- W2510147699 abstract "There are two general problems related to finite dynamical systems (FDS): the analysis and the synthesis (also known as the reverse engineering ) problems. In the former, we are interested in uncovering the sequential structure of a given FDS. In the latter, given a prescribed structure, we have to find an appropriate FDS that accomplishes the intended behavior. In this work we reverse engineer FDSs related to two recent applications. One is the problem of finding an optimal linear (i.e., a matrix) FDS over the integers mod a prime p to efficiently compute FFTs with linear symmetries. For this, we propose O(p 2 log p) and O(p 3 log p) time algorithms for the two and three dimensional cases as opposed to O(p6) and O(p12) time of exhaustive searchs, respectively. Also, we characterize those important cases for which the symmetric FFT with prime edge-length can be computed through a single cyclic convolution. For the second problem, the reverse engineering problem in bioinformatics, we study and compare two finite field models for genetic networks and provide algorithms for converting one model into the other via a DFT. Also, we develop efficient methods for performing arithmetic over finite fields. We propose a new efficient parallel algorithm based on the Chinese remaindering theorem to interpolate over finite fields." @default.
- W2510147699 created "2016-09-16" @default.
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- W2510147699 date "2006-01-01" @default.
- W2510147699 modified "2023-10-16" @default.
- W2510147699 title "On some algorithms for reverse engineering certain finite dynamical systems" @default.
- W2510147699 hasPublicationYear "2006" @default.
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