Pomset languages recognized by higher-dimensional automata are regular iff inverse images of functors to finite categories and FO-definable iff recognized by aperiodic categories, generalizing McNaughton-Papert.
Aiswarya, Amaldev Manuel, and Saina Sunny
2 Pith papers cite this work. Polarity classification is still indexing.
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The edit distance between finite-valued transducers is computable.
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Algebraic Characterization of FO-definable Languages of Higher-Dimensional Automata
Pomset languages recognized by higher-dimensional automata are regular iff inverse images of functors to finite categories and FO-definable iff recognized by aperiodic categories, generalizing McNaughton-Papert.
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Edit Distance of Finite-Valued Transducers
The edit distance between finite-valued transducers is computable.