More Structural Characterizations of Some Subregular Language Families by Biautomata

TL;DR

This paper explores structural restrictions on biautomata, comparing their induced language families with those from deterministic finite automata, revealing cases of equivalence and difference in language characterization.

Contribution

It provides new insights into how structural properties of biautomata influence the classes of languages they recognize, highlighting differences from deterministic finite automata.

Findings

Permutation-freeness yields equivalent language classes for DFA and biautomata.

Strongly permutation-freeness leads to different language classes: definite languages for DFA, finite and co-finite for biautomata.

Structural restrictions on biautomata align with known language family landscapes.

Abstract

We study structural restrictions on biautomata such as, e.g., acyclicity, permutation-freeness, strongly permutation-freeness, and orderability, to mention a few. We compare the obtained language families with those induced by deterministic finite automata with the same property. In some cases, it is shown that there is no difference in characterization between deterministic finite automata and biautomata as for the permutation-freeness, but there are also other cases, where it makes a big difference whether one considers deterministic finite automata or biautomata. This is, for instance, the case when comparing strongly permutation-freeness, which results in the family of definite language for deterministic finite automata, while biautomata induce the family of finite and co-finite languages. The obtained results nicely fall into the known landscape on classical language families.