Hypercodes in Deterministic and Slender 0L Languages

In an infinite sequence of words over a finite alphabet some word must be embedded in a later word. In a D 0 L sequence such an embedding leads to a decomposition of the language into a finite language and a finite number of D O L languages for which the associated sequences are embedding chains. A language possessing such a decomposition has a bound for the size of the hypercodes (= embedding anti-chains) it can contain. Certain largest hypercodes related to D 0 L systems and languages are characterized. These characterizations provide methods for showing that languages are not D 0 L and for showing that pairs of D 0 L systems are not equivalent. A new class of 0 L languages, the slender languages, is introduced. This class contains the finite 0 L languages and the deterministic 0 L languages. Our key decomposition results are stated for slender languages.