Publications (5)1.31 Total impact
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ABSTRACT: We examine questions involving nondeterministic finite automata where all states are final, initial, or both initial and final. First, we prove hardness results for the nonuniversality and inequivalence problems for these NFAs. Next, we characterize the languages accepted. Finally, we discuss some state complexity problems involving such automata.  [Show abstract] [Hide abstract]
ABSTRACT: Carpi constructed an infinite word over a 4letter alphabet that avoids squares in all subsequences indexed by arithmetic progressions of odd difference. We show a connection between Carpi’s construction and the paperfolding words. We extend Carpi’s result by constructing uncountably many words that avoid squares in arithmetic progressions of odd difference. We also construct infinite words avoiding overlaps and infinite words avoiding all sufficiently large squares in arithmetic progressions of odd difference. We use these words to construct labelings of the 2dimensional integer lattice such that any line through the lattice encounters a squarefree (resp. overlapfree) sequence of labels. 
Conference Paper: The Frobenius Problem in a Free Monoid.
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ABSTRACT: The classical Frobenius problem over N is to compute the largest integer g not representable as a nonnegative integer linear combination of nonnegative integers x1; x2; : : : ; xk, where gcd(x1; x2; : : : ; xk) = 1. In this paper we consider novel generaliza tions of the Frobenius problem to the noncommutative setting of a free monoid. Unlike the commutative case, where the bound on g is quadratic, we are able to show exponential or subexponential behavior for several analogues of g, with the precise bound depending on the particular measure chosen. 
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ABSTRACT: The classical Frobenius problem is to compute the largest number g not representable as a nonnegative integer linear combination of nonnegative integers x_1, x_2, ..., x_k, where gcd(x_1, x_2, ..., x_k) = 1. In this paper we consider generalizations of the Frobenius problem to the noncommutative setting of a free monoid. Unlike the commutative case, where the bound on g is quadratic, we are able to show exponential or subexponential behavior for an analogue of g, depending on the particular measure chosen.
Publication Stats
38  Citations  
1.31  Total Impact Points  
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20072008

University of Waterloo
 David R. Cheriton School of Computer Science
Waterloo, Ontario, Canada
