The complexity of the max word problem
We study the complexity of the max word problem for matrices, a variation of the well-known word problem for matrices. We show that the problem is NP-complete, and cannot be approximated within any constant factor, unless P=NP. We describe applications of this result to probabilistic finite state automata, rational series and k-regular sequences. Our proof is novel in that it employs the theory of interactive proof systems, rather than a standard reduction argument. As another consequence of our results, we characterize NP exactly in terms of one-way interactive proof systems.
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