To simplify the task of proving termination of term rewriting systems, several elimination methods, such as the dummy elimination, the distribution elimination, the general dummy elimination and the improved general dummy elimination, have been proposed. In this paper, we show that the argument ltering method combining with the dependency pair technique is essential in all the above elimination methods. We present remarkable simple proofs for the soundness of these elimination methods based on this observation. Moreover, we propose a new elimination method, called the argument ltering transformation, which is not only more powerful than all the other elimination methods but also especially useful to make clear the essential relation hidden behind these methods.

We introduce a typed π-calculus where strong normalisation is ensured by typability. Strong normalisation is a useful property in many computational contexts, including distributed systems. In spite of its simplicity, our type discipline captures a wide class of converging name-passing interactive behaviour. The proof of strong normalisability combines methods from typed l-calculi and linear logic with process-theoretic reasoning. It is adaptable to systems involving state and other extensions. Strong normalisation is shown to have significant consequences, including finite axiomatisation of weak bisimilarity, a fully abstract embedding of the simply-typed l-calculus with products and sums and basic liveness in interaction.

In this paper we investigate the concept of simple termination. A term rewriting system is called simply terminating if its termination can be proved by means of a simplification order. The basic ingredient of a simplification order is the subterm property, but in the literature two different definitions are given: one based on (strict) partial orders and another one based on preorders (or quasi-orders). We argue that there is no reason to choose the second one, while the first one has certain advantages. Simplification orders are known to be well-founded orders on terms over a finite signature. This important result no longer holds if we consider infinite signatures. Nevertheless, well-known simplification orders like the recursive path order are also well-founded on terms over infinite signatures, provided the underlying precedence is well-founded. We propose a new definition of simplification order, which coincides with the old one (based on partial orders) in case of finite signatu...

In this note we present a simple proof of a result of Toyama which states that the disjoint union of confluent term rewriting systems is confluent. 1985 Mathematics Subject Classification: 68Q50 1987 CR Categories: F.4.2 Key Words and Phrases: theory of computation, term rewriting systems, modularity, confluence Introduction The topic of modularity of properties of term rewriting systems has caught much attention recently. An introduction to this area can be found in Klop [6]. For an early survey one may consult Middeldorp [7]. Moreover, the topic has received a fruitful offspring in the study of the conservation of properties when adding algebraic rewrite rules to various (typed) lambda calculi, see e.g. Breazu-Tannen and Gallier [1, 2] and Jouannaud and Okada [5]. 5 Partially supported by ESPRIT Basic Research Action 3020, INTEGRATION. 6 Partially supported by ESPRIT Basic Research Action 3074, SEMAGRAPH. 7 Partially supported by grants from NWO, Vrije Universiteit Amsterdam...

We study convergent (terminating and confluent) presentations of n-categories. Using the notion of polygraph (or computad), we introduce the homotopical property of finite derivation type for n-categories, generalising the one introduced by Squier for word rewriting systems. We characterise this property by using the notion of critical branching. In particular, we define sufficient conditions for an n-category to have finite derivation type. Through examples, we present several techniques based on derivations of 2-categories to study convergent presentations by 3-polygraphs.

Copyright c ○ 2000 by Keiichirou KUSAKARI Recently, Arts and Giesl introduced the notion of dependency pairs, which gives effective methods for proving termination of term rewriting systems (TRSs). In this thesis, we extend the notion of dependency pairs to AC-TRSs, and introduce new methods for effectively proving AC-termination. Since it is impossible to directly apply the notion of dependency pairs to AC-TRSs, we introduce the head parts in terms and show an analogy between the root positions in infinite reduction sequences by TRSs and the head positions in those by AC-TRSs. Indeed, this analogy is essential for the extension of dependency pairs to AC-TRSs. Based on this analogy, we define AC-dependency pairs. To simplify the task of proving termination and AC-termination, several elimination transformations such as the dummy elimination, the distribution elimination, the general dummy elimination and the improved general dummy elimination, have been proposed. In this thesis, we show that the argument filtering method combined with the AC-dependency pair technique is essential in all the elimination transformations above. We present remarkable simple proofs for the soundness of these elimination transformations based on this observation. Moreover, we propose a new elimination transformation, called the argument filtering transformation, which is not only more powerful than all the other elimination transformations but also especially useful to make clear an essential relationship among them.

Graphs and graph transformations are natural means to describe systems of processes. Graphs represent structure of the system, and graph rewriting rules model dynamic behaviour. In this chapter, we illustrate the technique by describing Petri nets, statecharts, parallel logic programming, and systems of processes. Whereas description of Petri nets is based on usual graphs, statecharts lead us to hierarchical graphs, and parallel logic programming needs jungles. Finally, we combine different approaches to describe systems of processes. Topological structure is represented by a hypergraph. Local states and communication channels correspond to nodes that are labelled with parts of a global jungle playing the role of a shared data structure. The formal model takes advantage of comma-category approach allowing to change both the structure of graph and the contents of nodes consistently and to treat different graph structures as well as different labelling mechanisms in

Models are considered an essential step in capturing different system behaviors and simplifying the analysis required to check or improve the quality of software. Verification and testing of web software requires effective modeling techniques that address the specific challenges of web applications. In this study we survey 24 different modeling methods used in website verification and testing. Based on a short catalogue of desirable properties of web applications that require analysis, two different views of the methods are presented: a general categorization by modeling level, and a detailed comparison based on property coverage.