More Structural Characterizations of Some Subregular Language Families by Biautomata

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.Comment: In Proceedings AFL 2014, arXiv:1405.527

Maximally Atomic Languages

The atoms of a regular language are non-empty intersections of complemented and uncomplemented quotients of the language. Tight upper bounds on the number of atoms of a language and on the quotient complexities of atoms are known. We introduce a new class of regular languages, called the maximally atomic languages, consisting of all languages meeting these bounds. We prove the following result: If L is a regular language of quotient complexity n and G is the subgroup of permutations in the transition semigroup T of the minimal DFA of L, then L is maximally atomic if and only if G is transitive on k-subsets of 1,...,n for 0 <= k <= n and T contains a transformation of rank n-1.Comment: In Proceedings AFL 2014, arXiv:1405.527

Generalized Results on Monoids as Memory

We show that some results from the theory of group automata and monoid automata still hold for more general classes of monoids and models. Extending previous work for finite automata over commutative groups, we demonstrate a context-free language that can not be recognized by any rational monoid automaton over a finitely generated permutable monoid. We show that the class of languages recognized by rational monoid automata over finitely generated completely simple or completely 0-simple permutable monoids is a semi-linear full trio. Furthermore, we investigate valence pushdown automata, and prove that they are only as powerful as (finite) valence automata. We observe that certain results proven for monoid automata can be easily lifted to the case of context-free valence grammars.Comment: In Proceedings AFL 2017, arXiv:1708.0622