Georg Zetzsche

On erasing productions in random context grammars

Three open questions in the theory of regulated rewriting are addressed. The first is whether every permitting random context grammar has a non-erasing equivalent. The second asks whether the same is true for matrix grammars without appearance checking. The third concerns whether permitting random context grammars have the same generative capacity as matrix grammars without appearance checking. n nThe main result is a positive answer to the first question. For the other two, conjectures are presented. It is then deduced from the main result that at least one of the two holds.

Properties of Multiset Language Classes Defined by Multiset Pushdown Automata

The previously introduced multiset language classes defined by multiset pushdown automata are being explored with respect to their closure properties and alternative characterizations.

Multiset Pushdown Automata

Multiset finite Automata, a model equivalent to regular commutative grammars, are extended with a multiset store and the accepting power of this extended model of computation is investigated. This type of multiset automata come in two flavours, varying only in the ability of testing the storage for emptiness. This paper establishes normal forms and relates the derived language classes to each other as well as to known multiset language classes.

Erasing in Petri Net Languages and Matrix Grammars

It is shown that applying linear erasing to a Petri net language yields a language generated by a non-erasing matrix grammar. The proof uses Petri net controlled grammars. These are context-free grammars, where the application of productions has to comply with a firing sequence in a Petri net. Petri net controlled grammars are equivalent to arbitrary matrix grammars (without appearance checking), but a certain restriction on them (linear Petri net controlled grammars) leads to the class of languages generated by non-erasing matrix grammars. n nIt is also shown that in Petri net controlled grammars (with final markings and arbitrary labeling), erasing rules can be eliminated, which yields a reformulation of the problem of whether erasing rules in matrix grammars can be eliminated.

Labeled Step Sequences in Petri Nets

We compare various modes of firing transitions in Petri nets and investigate classes of languages specified by them. We define languages through steps, (i. e., sets of transitions), maximal steps, multi-steps, (i. e., multisets of transitions), and maximal multi-steps of transitions in Petri nets. However, by considering labeled transitions, we do this in a different manner than in [Burk 81a, Burk 83]. Namely, we allow only sets and multisets of transitions to form a (multi-)step, if they all share the same label. In a sequence of (multi-)steps, each of them contributes its label once to the generated word. Through different firing modes that allow multiple use of transitions in a single multi-step, we obtain a hierarchy of families of languages. Except for the maximal multi-steps all classes can be simulated by sequential firing of transitions.

The Complexity of Downward Closure Comparisons

The downward closure of a language is the set of all (not necessarily contiguous) subwords of its members. It is well-known that the downward closure of every language is regular. Moreover, recent results show that downward closures are computable for quite powerful system models. nOne advantage of abstracting a language by its downward closure is that then equivalence and inclusion become decidable. In this work, we study the complexity of these two problems. More precisely, we consider the following decision problems: Given languages

Petri Net Controlled Finite Automata

K

Language Classes Defined by Concurrent Finite Automata

and

PTL-separability and closures for WQOs on words

L

Unboundedness Problems for Languages of Vector Addition Systems.

from classes