title: Term Graph Rewriting and Strong Sequentiality
author: Sjaak Smetsers
This paper propagates the use of term graph rewriting systems as a formal
computational model. The definition of both term graphs and the reduction
relation on term graphs are more complex than their corresponding notions in
term rewriting systems. Consequently, it is often believed that reasoning about
term graph rewriting systems is inherently more difficult than reasoning about
term rewriting systems. In this paper we will show that it is very well possible
to investigate formal properties of term graph rewriting systems entirely within
the framework of these systems. First, we will establish a basic theory based on
graph homomorphisms and the term graph reduction relation. In this theory the
concepts of index and strong sequentiality are incorporated. Lastly, we will
prove that index reduction is normalising for the so-called strongly sequential
term graph rewriting systems.