Abstract

A OL system is called a quasi-deterministic OL system or a D'OL system for short if there is an integer C such that the cardinality of the set of words generated in n steps is less than C for every n . D'OL systems form a subfamily of the family of OL systems. It is shown that a OL system is effectively decidable whether it is a D'OL system or not and the derivations of a D'OL system are represented by the derivations of an HFDOL system. Using these results, the family of languages generated by D'OL systems is characterized in the families of HDOL languages, HFDOL languages, EFDOL languages, NDOL languages, DOL languages, and OL languages. It is also shown that the equivalence problem between context-free languages and the family of D'OL languages and the regularity and the context-freeness problems for the family of D'OL languages are decidable.

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