Unary weighted automata over the tropical semiring admit a polynomial-time computable quadratic-size union representation of deterministic automata, implying coNP-completeness of determinisation and register minimisation.
Papadimitriou and Mihalis Yannakakis
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Bounded comparison of transducers under Hamming distance is NL-complete for fixed k, co-NP-complete for binary k, DP-complete for exact distance k, with a tight quadratic bound on the maximum distance and logspace equivalence to the deviations problem.
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Representing One Letter Weighted Automata Over the Tropical Semiring
Unary weighted automata over the tropical semiring admit a polynomial-time computable quadratic-size union representation of deterministic automata, implying coNP-completeness of determinisation and register minimisation.
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Hamming distance between finite transducers
Bounded comparison of transducers under Hamming distance is NL-complete for fixed k, co-NP-complete for binary k, DP-complete for exact distance k, with a tight quadratic bound on the maximum distance and logspace equivalence to the deviations problem.