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| Title: | The Frobenius Problem in a Free Monoid |
| Authors: | Xu, Zhi |
| Keywords: | Frobenius problem
free monoid
co-finite
Kleene-star
combinatorics on words
de Bruijn graph |
| Approved Date: | 21-Aug-2009 |
| Date Submitted: | 2009 |
| Abstract: | Given positive integers c1,c2,...,ck with gcd(c1,c2,...,ck) = 1, the Frobenius problem (FP) is to compute the largest integer g(c1,c2,...,ck) that cannot be written as a non-negative integer linear combination of c1,c2,...,ck. The Frobenius problem in a free monoid (FPFM) is a non-commutative generalization of the Frobenius problem. Given words x1,x2,...,xk such that there are only finitely many words that cannot be written as concatenations of words in {x1,x2,...,xk}, the FPFM is to find the longest such words. Unlike the FP, where the upper bound g(c1,c2,...,ck)≤max 1≤i≤k ci2 is quadratic, the upper bound on the length of the longest words in the FPFM can be exponential in certain measures and some of the exponential upper bounds are tight. For the 2FPFM, where the given words over Σ are of only two distinct lengths m and n with 1 |
| Program: | Computer Science (Software Engineering) |
| Department: | School of Computer Science |
| Degree: | Doctor of Philosophy |
| URI: | http://hdl.handle.net/10012/4574 |
| Appears in Collections: | Electronic Theses and Dissertations (UW)
Faculty of Mathematics Theses and Dissertations
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