Term Graph Rewriting and Strong Sequentiality

This paper propagates the use of term graph rewriting systems as a formal computational model. The deenition 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 diicult 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.