The decreasing diagrams technique (van Oostrom, 1994) has been successfully used to prove confluence of rewrite systems in various ways; using rule-labelling (van Oostrom, 2008), it can also be applied directly to prove confluence of some linear term rewriting systems (TRSs) automatically. Some efforts for extending the rule-labelling are known, but non-left-linear TRSs are left beyond the scop...

We have developed an automated confluence prover for term rewriting systems (TRSs). This paper presents theoretical and technical ingredients that have been used in our prover. A distinctive feature of our prover is incorporation of several divide–and–conquer criteria such as those for commutative (Toyama, 1988), layer-preserving (Ohlebusch, 1994) and persistent (Aoto & Toyama, 1997) combinatio...

Building on recent interest in distributed logic programming, we take a model-theoretic approach to analyzing confluence of asynchronous distributed programs. We begin with a model-theoretic semantics for Dedalus and introduce the ultimate model, which captures non-deterministic eventual outcomes of distributed programs. After showing the question of confluence undecidable for Dedalus, we ident...

For each Painlevé system, we have a manifold, called the defining manifold, on which the system defines a uniform foliation. In this paper, we describe confluence processes in these manifolds as deformations of manifolds compatible to those in Painlevé systems.

Available online 13 March 2015

Asymptomatic enamel and dentin cracks can pose a risk for multiple pathological and undesired consequences if intervention is postponed. This article reviews asymptomatic enamel and dentin cracks, and presents current management approaches utilized by a sample of general dentists. Becoming familiar with all forms of asymptomatic enamel and dentin cracks is crucial to adopting a proactive approa...

Dental enamel is highly transparent at near-IR wavelengths and several studies have shown that these wavelengths are well suited for optical transillumination for the detection and imaging of tooth decay. We hypothesize that these wavelengths are also well suited for imaging cracks in teeth. Extracted teeth with suspected cracks were imaged at several wavelengths in the near-IR from 1300-1700-n...

A new algorithm is described which extends the material point method (MPM) to allow explicit cracks within the model material. Conventional MPM enforces velocity and displacement continuity through its background grid. This approach is incompatible with cracks which are displacement and velocity discontinuities. By allowing multiple velocity fields at special nodes near cracks, the new method (...

In the logic based framework of knowledge representation and reasoning many operators have been defined in order to capture different kinds of change : revision, update, merging and many others. There are close links between revision, update, and merging. Merging operators can be considered as extensions of revision operators to multiple belief bases. And update operators can be considered as p...

We present a novel proof of Toyama’s famous modularity of confluence result for term rewriting systems. Apart from being short and intuitive, the proof is modular itself in that it factors through the decreasing diagrams technique for abstract rewriting systems, is constructive in that it gives a construction for the converging rewrite sequences given a pair of diverging rewrite sequences, and ...