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.
On finite monoids having on ly trivial subgroups
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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.
- The $\mathsf{AC}^0$-Complexity Of Visibly Pushdown Languages