dc.contributor.author Vasiga, Troy Michael John dc.date.accessioned 2008-08-26 18:46:06 (GMT) dc.date.available 2008-08-26 18:46:06 (GMT) dc.date.issued 2008-08-26T18:46:06Z dc.date.submitted 2008 dc.identifier.uri http://hdl.handle.net/10012/3895 dc.description.abstract CPU's are unreliable: at any point in a computation, a bit may be altered with some (small) probability. This probability may seem negligible, but for large calculations (i.e., months of CPU time), the likelihood of an error being introduced becomes increasingly significant. Relying on this fact, this thesis defines a statistical measure called robustness, and measures the robustness of several number-theoretic and algebraic algorithms. en Consider an algorithm A that implements function f, such that f has range O and algorithm A has range O' where O⊆O'. That is, the algorithm may produce results which are not in the possible range of the function. Specifically, given an algorithm A and a function f, this thesis classifies the output of A into one of three categories: 1. Correct and feasible -- the algorithm computes the correct result, 2. Incorrect and feasible -- the algorithm computes an incorrect result and this output is in O, 3. Incorrect and infeasible -- the algorithm computes an incorrect result and output is in O'\O. Using probabilistic measures, we apply this classification scheme to quantify the robustness of algorithms for computing primality (i.e., the Lucas-Lehmer and Pepin tests), group order and quadratic residues. Moreover, we show that typically, there will be an "error threshold" above which the algorithm is unreliable (that is, it will rarely give the correct result). dc.language.iso en en dc.publisher University of Waterloo en dc.subject algorithm analysis en dc.subject error detection en dc.subject primality testing en dc.title Error Detection in Number-Theoretic and Algebraic Algorithms en dc.type Doctoral Thesis en dc.comment.hidden Used the latex e-version of the template in LaTeX in creating the PDF. en dc.pending false en dc.subject.program Computer Science en uws-etd.degree.department School of Computer Science en uws-etd.degree Doctor of Philosophy en uws.typeOfResource Text en uws.peerReviewStatus Unreviewed en uws.scholarLevel Graduate en
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