On almost cylindrical languages and the decidability of the D0L and PWD0L primitivity problems

AbstractPrimitive words and their properties have always been of fundamental importance in the study of formal language theory. Head and Lando in Periodic D0L Languages proposed the idea of deciding whether or not a given D0L language has the property that every word in it is a primitive word. After reducing the general problem to the case in which h is injective, it will be shown that primitivity is decidable when ((A)h)∗ is an almost cylindrical set. Moreover, in this case, it is shown that the set of words which generate primitive sequences (given a particular D0L scheme) is an algorithmically constructible context-sensitive language. An undecidability result for the PWD0L primitivity problem and decidability results for cases of the RWD0L primitivity problem are also given

On test sets for checking morphism equivalence on languages with fair distribution of letters

AbstractA test set for a language L is a finite subset T of L with the property that each pair of morphisms that agrees on T also agrees on L. Some results concerning test sets for languages with fair distribution of letters are presented. The first result is that every D0L language with fair distribution of letters has a test set. The second result shows that every language L with fair distribution has a test set relative to morphisms g, h which have bounded balance on L. These results are generalizations of results of Culik II and Karhumäki (1983)

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

LANGUAGE CONTACT AND COVERT PROMINENCE IN THE SḤERĒT-JIBBĀLI LANGUAGE OF OMAN

This thesis reports on a phonetic production study, the results of which support the existence of a complex word-prosodic system for the Sḥerēt-Jibbāli language of Dhofar, Oman. In the language, stress seems to co-occur in some lexical items with a high tone. In the discussion, a mechanism for the emergence of this system is proposed as the reflex of a typological feature held in common with the related language, Soqotri, and as justification for an Eastern Modern South Arabian subgroup consisting of Sḥerēt-Jibbāli and Soqotri

On a generalization of Abelian equivalence and complexity of infinite words

In this paper we introduce and study a family of complexity functions of infinite words indexed by k in Z^+ U {+infinity}. Let k in Z^+ U {+infinity} and A be a finite non-empty set. Two finite words u and v in A* are said to be k-Abelian equivalent if for all x in A* of length less than or equal to k, the number of occurrences of x in u is equal to the number of occurrences of x in v. This defines a family of equivalence relations sim_k on A*, bridging the gap between the usual notion of Abelian equivalence (when k = 1) and equality (when k = +infinity). We show that the number of k-Abelian equivalence classes of words of length n grows polynomially, although the degree is exponential in k. Given an infinite word omega in A^N, we consider the associated complexity function P^(k)_omega : N -> N which counts the number of k-Abelian equivalence classes of factors of omega of length n. We show that the complexity function P_k is intimately linked with periodicity. More precisely we define an auxiliary function q^k : N -> N and show that if P^(k)_omega(n) < q^k(n) for some k in Z^+ U {+infinity} and n >= 0, then omega is ultimately periodic. Moreover if omega is aperiodic, then P^(k)_omega(n) = q^k(n) if and only if omega is Sturmian. We also study k-Abelian complexity in connection with repetitions in words. Using Szemeredi's theorem, we show that if omega has bounded k-Abelian complexity, then for every D subset of N with positive upper density and for every positive integer N, there exists a k-Abelian N-power occurring in omega at some position j in D