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dc.contributor.advisorBollman, Dorothy
dc.contributor.authorOrozco, Edusmildo
dc.description.abstractThere 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. On 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(p2logp) and o(p3logp) time algorithms for the two and three dimensional cases as opposed to O(p6) and O(p12) time of exhaustive searches, respectively. Also, we characterize those important cases for which he 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 in the Chines remaindering theorem to interpolate over finite fields.en_US
dc.description.sponsorshipThis work was partially supported by the National Science Foundation Grant No. 9817642 under the AGEP Program and Grant No. EIA 99777071 under the precise Program.en_US
dc.subjectReverse engineeringen_US
dc.subjectDynamical systemsen_US
dc.titleOn some algorithms for reverse engineering certain finite dynamical systemsen_US
dc.rights.licenseAll rights reserveden_US
dc.rights.holder(c) 2005 Jose R. Ortiz-Ubarrien_US
dc.contributor.committeeMorena, Oscar
dc.contributor.committeeRivera, Wilson
dc.contributor.committeeRodriguez, Domingo
dc.contributor.committeeSeguel, Jaime
dc.contributor.committeeGooransarab, Haedeh
dc.contributor.representativeBonaventura, Joseph and Information Sciences and Engineeringen_US
dc.contributor.collegeCollege of Engineeringen_US
dc.contributor.departmentDepartment of Electrical and Computer Engineeringen_US

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