Fixed Point Languages, Equality Languages, and Representation of Recursively Enumerable Languages

Equality sets for recursively enumerable languages

We consider shifted equality sets of the form EG(a, g1, g2) = {w | g1(w) = ag2(w)}, where g1 and g2 are nonerasing morphisms and a is a letter. We are interested in the family consisting of the languages h(EG(J)), where h is a coding and EG(J) is a shifted equality set. We prove several closure properties for this family. Moreover, we show that every every recursively enumerable language L ⊆ A∗...

Equality Languages and Fixed Point Languages

This paper considers equality hmguages and fixed-point languages of homomorphisms and deterministic gsm mappings. It provides some basic properties of these classes of languages. Vfe introduce a new subclass of dgsm mappings, the so-called symmetric dgsm mappings. We prove that (unlike for arbitrary dgsm mappings) their fixed-point languages are regular but not effectively obtainable. This resu...

Polynomial Generators of Recursively Enumerable Languages

Partial Learning of Recursively Enumerable Languages

This paper studies several typical learning criteria in the model of partial learning of r.e. sets in the recursion-theoretic framework of inductive inference. Its main contribution is a complete picture of how the criteria of confidence, consistency and conservativeness in partial learning of r.e. sets separate, also in relation to basic criteria of learning in the limit. Thus this paper const...

Grammar Systems as Language Analyzers and Recursively Enumerable Languages

We consider parallel communicating grammar systems which consist of several grammars and perform derivation steps, where each of the grammars works in a parallel and synchronized manner on its own sentential form, and communication steps, where a transfer of sentential forms is done. We discuss accepting and analyzing versions of such grammar systems with context-free productions and present ch...