Optimal spectral-norm approximate minimization of weighted finite automata
arXiv preprint arXiv:2102.06860, 2021•arxiv.org
We address the approximate minimization problem for weighted finite automata (WFAs) with
weights in $\mathbb {R} $, over a one-letter alphabet: to compute the best possible
approximation of a WFA given a bound on the number of states. This work is grounded in
Adamyan-Arov-Krein Approximation theory, a remarkable collection of results on the
approximation of Hankel operators. In addition to its intrinsic mathematical relevance, this
theory has proven to be very effective for model reduction. We adapt these results to the …
weights in $\mathbb {R} $, over a one-letter alphabet: to compute the best possible
approximation of a WFA given a bound on the number of states. This work is grounded in
Adamyan-Arov-Krein Approximation theory, a remarkable collection of results on the
approximation of Hankel operators. In addition to its intrinsic mathematical relevance, this
theory has proven to be very effective for model reduction. We adapt these results to the …
We address the approximate minimization problem for weighted finite automata (WFAs) with weights in , over a one-letter alphabet: to compute the best possible approximation of a WFA given a bound on the number of states. This work is grounded in Adamyan-Arov-Krein Approximation theory, a remarkable collection of results on the approximation of Hankel operators. In addition to its intrinsic mathematical relevance, this theory has proven to be very effective for model reduction. We adapt these results to the framework of weighted automata over a one-letter alphabet. We provide theoretical guarantees and bounds on the quality of the approximation in the spectral and norm. We develop an algorithm that, based on the properties of Hankel operators, returns the optimal approximation in the spectral norm.
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