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The recently introduced model of transducing by observing is compared with traditional models for computing transductions on the one hand and the recently introduced restarting transducers on the other hand. Most noteworthy, transducing observer systems with length-reducing rules are almost equivalent to RRWW-transducers. With painter rules we obtain a larger class of relations that additionally includes nearly all rational relations.
Duplication is the replacement of a factor within a word by . This operation can be used iteratively to generate
languages starting from words or sets of words. By undoing duplications, one can eventually
reach a square-free word, the original word's duplication root. The duplication root is unique, if the length of duplications is fixed.
Based on these unique roots we define the concept of duplication code. Elementary properties are stated, then the conditions under which infinite duplication...
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