In this paper we consider the computational complexity of the following problems: given a DFA or NFA representing a regular language L over a finite alphabet Σ, is the set of all prefixes (resp., suffixes, factors, subwords) of all words of L equal t

The classical Frobenius problem over ${mathbb N}$ is to compute the largest integer $g$ not representable as a non-negative integer linear combination of non-negative integers $x_1, x_2, ldots, x_k$, where $gcd(x_1, x_2, ldots, x_k) = 1$. In this paper we consider novel 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 several analogues of $g$, with the precise bound depending on the particular measure chosen.