First-order translations have recently been characterized as the maps computed by aperiodic single-valued nondeterministic finite transducers (NFTs). It is shown here that this characterization lifts to “V-translations” and “V-single-valued-NFTs”, where V is an arbitrary monoid pseudovariety. More strikingly, 2-way V-machines are introduced, and the following three models are shown exactly equivalent to Eilenberg’s classical notion of a bimachine when V is a group variety or when V is the variety of aperiodic monoids: V-translations, V-single-valued-NFTs and 2-way V-transducers.
CITATION STYLE
McKenzie, P., Schwentick, T., Thérien, D., & Vollmer, H. (2000). The many faces of a translation. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 1853, pp. 890–901). Springer Verlag. https://doi.org/10.1007/3-540-45022-x_75
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