Adult Languages of Propagating Systems with Restricted Parallelism

abstract Various rewriting mechanisms can be thought of as functions mapping words w to nite sets of words W. The adult language of (; !) is the set of words w which are xed points of , i.e. (w) = fwg, and reachable from a start word or axiom !, i.e. w 2 n (!) for some n 2 N 0. Interestingly, for systems without the table mechanism, the degree of parallelism does not aaect the generative capacity when considering adult languages. On the other hand, considering systems with tables, the families of adult languages equal the corresponding families of languages with extensions. Furthermore, some open problems from 2,7,27 are attacked by using propagating ordered grammars. The proofs of the results mentioned in this paper appear elsewhere. 8