Weakly recognizing morphisms from free semigroups onto finite semigroups are a classical way for defining the class of ω-regular languages, i.e., a set of infinite words is weakly recognizable by such a morphism if and only if it is accepted by some Büchi automaton. We consider the descriptional complexity of various constructions for weakly recognizing morphisms. This includes the conversion f...

The communication structure of parallel communicating grammar systems (PCGS) considered as the descriptional complexity of PCGS is investigated here. The aim of the paper is to compare computational power of PCGS’s with respect to their communication structure. Investigating the generation of the languages over one-letter alphabet the communication structures dags(directed acyclic graphs) and c...

We prove that the set of properties describable by a uniform sequence of rst-order sentences using at most k + 1 distinct variables is exactly equal to the set of properties checkable by a Turing machine in DSPACEn k ] (where n is the size of the universe). This set is also equal to the set of properties describable using an iterative deenition for a nite set of relations of arity k. This is a ...

We aim to generalize Büchi’s fundamental theorem on the coincidence of recognizable and MSO-definable languages to a weighted timed setting. For this, we investigate weighted timed automata and show how we can extend Wilke’s relative distance logic with weights taken from an arbitrary semiring. We show that every formula in our logic can effectively be transformed into a weighted timed automato...

Our goal is to study the complexity of infinite binary recursive sequences. We introduce several measures of the quantity of information they contain. Some measures are based on size of programs that generate the sequence, the others are based on the Kolmogorov complexity of its finite prefixes. The relations between these complexity measures are established. The most surprising among them are ...