Minimal deterministic finite automata (dfas) can be reduced further at the expense of a finite number of errors. Recently, such minimization algorithms have been improved to run in time O(n log n), where n is the number of states of the input dfa, by [Gawrychowski and Jeż: Hyper-minimisation made efficient. Proc. Mfcs, Lncs 5734, 2009] and [Holzer and Maletti: An n log n algorithm for hyper-minimizing a (minimized) deterministic automaton. Theor. Comput. Sci. 411, 2010]. Both algorithms return a dfa that is as small as possible, while only committing a finite number of errors. These algorithms are further improved to return a dfa that commits the least number of errors at the expense of an increased (quadratic) run-time. This solves an open problem of [Badr, Geffert, and Shipman: Hyper-minimizing minimized deterministic finite state automata. Rairo Theor. Inf. Appl. 43, 2009]. In addition, an experimental study on random automata is performed and the effects of the existing algorithms and the new algorithm are reported.

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We present the IMS-TTT submission to WMT14, an experimental statistical treeto-tree machine translation system based on the multi-bottom up tree transducer including rule extraction, tuning and decoding. Thanks to input parse forests and a "no pruning" strategy during decoding, the obtained translations are competitive. The drawbacks are a restricted coverage of 70% on test data, in part due to exact input parse tree matching, and a relatively high runtime. Advantages include easy redecoding with a different weight vector, since the full translation forests can be stored after the first decoding pass.

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Hyper-minimization is a state reduction technique that allows a finite change in the semantics. The theory for hyper-minimization of deterministic weighted tree automata is provided. The presence of weights slightly complicates the situation in comparison to the unweighted case. In addition, the first hyper-minimization algorithm for deterministic weighted tree automata, weighted over commutative semifields, is provided together with some implementation remarks that enable an efficient implementation. In fact, the same run-time O(m log n) as in the unweighted case is obtained, where m is the size of the deterministic weighted tree automaton and n is its number of states.Comment: In Proceedings AFL 2014, arXiv:1405.527