Abstract
We consider how to edit strings from a source language so that the edited strings belong to a target language, where the languages are given as deterministic finite automata. Non-streaming (or offline) transducers perform edits given the whole source string. We show that the class of deterministic one-pass transducers with registers along with increment and min operation suffices for computing optimal edit distance, whereas the same class of transducers without the min operation is not sufficient. Streaming (or online) transducers perform edits as the letters of the source string are received. We present a polynomial time algorithm for the partial-repair problem that given a bound α asks for the construction of a deterministic streaming transducer (if one exists) that ensures that the ‘maximum fraction’ η of the strings of the source language are edited, within cost α, to the target language.
The research was supported by Austrian Science Fund (FWF) Grant No P 23499-N23, FWF NFN Grant No S11407-N23 (RiSE), ERC Start grant (279307: Graph Games), and Microsoft faculty fellows award. Thanks to Gabriele Puppis for suggesting the problem of identifying a deterministic transducer to compute the optimal cost, and to Martin Chmelik for his comments on the introduction.
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Chatterjee, K., Chaubal, S., Rubin, S. (2013). How to Travel between Languages. In: Dediu, AH., Martín-Vide, C., Truthe, B. (eds) Language and Automata Theory and Applications. LATA 2013. Lecture Notes in Computer Science, vol 7810. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37064-9_20
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DOI: https://doi.org/10.1007/978-3-642-37064-9_20
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