We construct finite complete rewriting systems for two large classes of Artin groups: those of finite type, and those whose defining graphs are based on trees. The constructions in the two cases are quite different; while the construction for Artin groups of finite type uses normal forms introduced through work on complex hyperplane arrangements, the rewriting systems for Artin groups based on ...

We consider the problems of conjunctive query answering and rewriting for information integration systems in which a Description Logic ontology is used to provide a global view of the data. We present a resolution-based query rewriting algorithm for DL-Lite ontologies, and use it to show that query answering in this setting is NLogSpacecomplete with respect to data complexity. We also show that...

Prefix iteration a∗x is added to Minimal Process Algebra (MPAδ), which is a subalgebra of BPAδ equivalent to Milner’s basic CCS. We present a finite equational axiomatization for MPA∗ δ , and prove that this axiomatization is complete with respect to strong bisimulation equivalence. To obtain this result, we set up a term rewriting system, based on the axioms, and show that bisimilar terms have...

Algebraic speciications allied to rewriting are used more and more often in design and logical prototyping of programs. We show how these techniques can be applied to a basic problem in computational geometry, namely the construction of planar subdivisions. We build up a simple, complete and convergent system of rules to cope with this problem and show how it is transformed to describe concrete...

We present two new transformation techniques for proving termination of context-sensitive rewriting. Our rst method is simple, sound, and more powerful than previously suggested transformations. However, it is not complete, i.e., there are terminating context-sensitive rewrite systems that are transformed into non-terminating term rewrite systems. The second method that we present in this paper...

Narrowing is a universal unification procedure for equational theories defined by a canonical term rewriting system. In its original form it is extremely inefficient. Therefore, many optimizations have been proposed during the last years. In this paper, we present the narrowing strategies for arbitrary canonical systems in a uniform framework and introduce the new narrowing strategy LSE narrowi...

It is well-known that a term rewriting system can be faithfully described by a cartesian 2-category, where horizontal arrows represent terms, and cells represent rewriting sequences. In this paper we propose a similar, original 2-categorical presentation for term graph rewriting. Building on a result presented in 8], which shows that term graphs over a given signature are in one-to-one correspo...

We study the problem of how to compute boolean abstraction solution set a linear equation system over positive reals. call ϕ exact for if abstract interpretation structure booleans is equal Abstract thus complete when restricted systems, while it not more generally. present new rewriting algorithm that makes systems preserving solutions The based on elementary modes system. computation may requ...

Let E be a rst-order equational theory. A translation of typed higher-order E-uniication problems into a typed combinatory logic framework is presented and justiied. The case in which E admits presentation as a convergent term rewriting system is treated in detail: in this situation, a modiication of ordinary narrowing is shown to be a complete method for enumerating higher-order E-uniiers. In ...