Accepting grammars and systems

We investigate several kinds of regulated rewriting (programmed,
matrix, with regular control, ordered, and variants thereof) and
of parallel rewriting mechanisms (Lindenmayer systems, uniformly
limited Lindenmayer systems, limited Lindenmayer systems and
scattered context grammars) as accepting devices, in contrast
with the usual generating mode.

In some cases, accepting mode turns out to be just as powerful as
generating mode, e.g. within the grammars of the Chomsky
hierarchy, within random context, regular control, L systems,
uniformly limited L systems, scattered context. Most of these
equivalences can be proved using a metatheorem on so-called
context condition grammars. In case of matrix grammars and
programmed grammars without appearance checking, a straightforward
construction leads to the desired equivalence result.
Interestingly, accepting devices are (strictly) more powerful than
their generating counterparts in case of ordered grammars,
programmed and matrix grammars with appearance checking (even
programmed grammarsm with unconditional transfer), and 1lET0L
systems. More precisely, if we admit erasing productions, we
... mehrarrive at new characterizations of the recursivley enumerable
languages, and if we do not admit them, we get new
characterizations of the context-sensitive languages.

Moreover, we supplement the published literature showing:

- The emptiness and membership problems are recursivley solvable
for generating ordered grammars, even if we admit erasing
productions.
- Uniformly limited propagating systems can be simulated by
programmed grammars without erasing and without appearance
checking, hence the emptiness and membership problems are
recursively solvable for such systems.
- We briefly discuss the degree of nondeterminism and the
degree of synchronization for devices with limited parallelism.