On images of D0L and DT0L power series

AbstractThe D0L and DT0L power series are generalizations of D0L and DT0L languages. We continue the study of these series by investigating various decidability questions concerning the images of D0L and DT0L power series

Commuting upper triangular binary morphisms

A morphism $g$ from the free monoid $X^*$ into itself is called upper triangular if the matrix of $g$ is upper triangular. We characterize all upper triangular binary morphisms $g_1$ and $g_2$ such that $g_1g_2=g_2g_1$.Comment: 14 page

On Lindenmayerian algebraic sequences

AbstractWe define and study Lindenmayerian algebraic sequences. These sequences are a generalization of algebraic sequences, k-regular sequences and automatic sequences

Easy cases of the D0L sequence equivalence problem

AbstractTo test the equivalence of two binary D0L sequences it suffices to compare the first four terms of the sequences. We introduce a larger class of D0L systems for which sequence equivalence can be decided by considering the first ten initial terms

On D0L systems with finite axiom sets

We give a new solution for the language equivalence problem of D0L systems with finite axiom sets by using the decidability of the equivalence problem of finite valued transducers on HDT0L languages proved by Culik II and Karhumäki

Marked D0L systems and the 2n-conjecture

AbstractWe show that to test the equivalence of two D0L sequences over an n-letter alphabet generated by marked morphisms it suffices to compare the first 2n+1 initial terms of the sequences. Under an additional condition it is enough to consider the 2n initial terms

Rational series with high image complexity

By using the universal Diophantine representation of recursively enumerable sets of positive integers due to Matiyasevich we construct a Z-rational series gamma Over a binary alphabet X which has a maximal image complexity in the sense that all recursively enumerable sets of positive integers are obtained as the sets of positive coefficients of the series w(-1)gamma where w. X-*. As a consequence we obtain various undecidability results for Z-rational series

Petolintuvuosi 2021 - sinnitellen kohti seuraavaa

Non peer reviewe