On the subword complexity of square-free DOL languages

AbstractThe subword complexity of a language K is the function which to every positive integer n assigns the number of different subwords of length n occuring in words of K. A language K is square-free if no word in it contains a subword of the form xx where x is a nonempty word. The (best) upper and lower bounds on the subword complexity of infinite square-free DOL languages are established

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

The generating function of the number of subpatterns of a DOL sequence

AbstractThe generating function of the number of subpatterns of a DOL sequence is shown to be rational. The computation of the generating function is based on a recursion formula which expresses this function by the generating functions of subpatterns of smaller length and by the Magnus transform of the homomorphism

On standard locally catenative L schemes

AbstractA standard locally catenative L scheme extracts the essential feature of the locally catenative property. We investigate conditions under which a standard locally catenative L scheme has multiple locally catenative L systems

On the decidability of homomorphism equivalence for languages

AbstractWe consider decision problems of the following type. Given a language L and two homomorphisms h1 and h2, one has to determine to what extent h1 and h2 agree on L. For instance, we say that h1 and h2 are equivalent on L if h1(ω) = h2(ω) holds for each ω ε L. In our main theorem we present an algorithm for deciding whether two given homomorphisms are equivalent on a given context-free language. This result also gives an algorithm for deciding whether the translations defined by two deterministic gsm mappings agree on a given context-free language

The decidability of the equivalence problem for DOL-systems

The language and sequence equivalence problem for DOL-systems is shown to be decidable. In an algebraic formulation the sequence equivalence problem for DOL-systems can be stated as follows: Given homomorphisms h1 and h2 on a free monoid Σ* and a word σ from Σ*, is h1n(σ) = h2n(σ) for all n ⩾ 0