Annual Report 2010 - Fachgruppe Informatik an der RWTH Aachen ...

Reachability over Word Rewriting Systems
Jan-Henrik Altenbernd
Word rewriting systems have been studied over the last century under several aspects. In the
beginning, they were considered as a framework for the representation of computation
processes and as a tool for generating formal languages. In more recent years, they have also
been investigated as a mechanism to represent infinite graphs by a finite formalism. This
thesis has its main focus in the latter domain.
In the first part of the thesis, we investigate mixed prefix / suffix rewriting (MPSR) systems,
which combine prefix and suffix rewriting in a nondeterministic way. We study central
algorithmic properties of the graphs that can be generated by such systems, with an emphasis
on the reachability problem (as a master problem in model-checking), and we determine the
connection between the c1asses of such graphs and other well-studied graph classes, such as
the classes of prefix recognizable and of automatic graphs. Furthermore, we study the class of
trace languages of graphs that are generated by MPSR systems, and we show that this class
strictly includes the class of context-free languages, and is itself properly included in the class
of context-sensitive languages.
In the second part of the thesis, we introduce and investigate tagged infix rewriting (TIR)
systems, which extend the MPSR systems, and which use special markers for a restricted
form of infix rewriting. We show that in their basic form, where the markers may not be
rewritten, TIR and MPSR systems share a number of model-cheeking properties, and we
obtain analogous results concerning their languages.
We also study two variants of TIR systems. For the first, where markers may be removed by
rewriting steps, we show that such systems preserve regularity of languages under rewriting,
by adapting the saturation method as known for pushdown systems. In the second variant,
where markers may be added by rewriting steps, this does not hold; however, we show that an
algorithmic reachability analysis is still possible.
Evaluators: Prof. Dr. Dr.h.c. Wolfgang Thomas,
Dr. habil. Didier Caucal (Université Paris Est)
Date of oral examination: 9 December 2009
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