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We study structural restrictions on biautomata such as, e.g., acyclicity,permutation-freeness, strongly permutation-freeness, and orderability, tomention a few. We compare the obtained language families with those induced bydeterministic finite automata with the same property. In some cases, it isshown that there is no difference in characterization between deterministicfinite automata and biautomata as for the permutation-freeness, but there arealso other cases, where it makes a big difference whether one considersdeterministic finite automata or biautomata. This is, for instance, the casewhen comparing strongly permutation-freeness, which results in the family ofdefinite language for deterministic finite automata, while biautomata inducethe family of finite and co-finite languages. The obtained results nicely fallinto the known landscape on classical language families.

More Structural Characterizations of Some Subregular Language Families by Biautomata