Term rewriting systems provide a versatile model of computation. An important property which allows to abstract from potential nondeterminism of parallel execution of the modelled program is confluence. In this paper we prove that confluence of a fairly large class of systems, namely right ground term rewriting systems, is decidable. We introduce a labelling of variables with colours and constr...

The notion of confluence is studied on the context of bigraphs. Confluence will be important in modelling real-world systems, both natural (as in biology) and artificial (as in pervasive computing). The paper uses bigraphs in which names have multiple locality; this enables a formulation of the lambda calculus with explicit substitutions. The paper reports work in progress, seeking conditions o...

Decreasing diagrams technique (van Oostrom, 1994) is a technique that can be widely applied to prove confluence of rewrite systems. To directly apply the decreasing diagrams technique to prove confluence of rewrite systems, rule-labelling heuristic has been proposed by van Oostrom (2008). We show how constraints for ensuring confluence of term rewriting systems constructed based on the rule-lab...

1. I n t r o d u c t i o n Many term rewriting systems and their modifications are considered in logic, automated theorem proving, and programming language [2,3,4,6,8,9]. A fundamental property of term rewriting systems is the confluence property. A few sufficient criteria for the confluence are well known [2,3,4,5,8,9]. However, if a term rewriting system is nonterminating and nonlinear, we kn...

It is well known that confluence and strong normalization are preserved when combining algebraic rewriting systems with the simply typed lambda calculus. It is equally well known that confluence fails when adding either the usual contraction rule for η, or recursion together with the usual contraction rule for surjective pairing. We show that confluence and strong normalization are modular prop...

The confluence model explains birth-order differences in intellectual performance by quantifying the changing dynamics within the family. Wichman, Rodgers, and MacCallum (2006) claimed that these differences are a between-family phenomenon--and hence are not directly related to birth order itself. The study design and analyses presented by Wichman et al. nevertheless suffer from crucial shortco...

The confluence of untyped λ-calculus with unconditional rewriting is now well understood. In this paper, we investigate the confluence of λ-calculus with conditional rewriting and provide general results in two directions. First, when conditional rules are algebraic. This extends results of Müller and Dougherty for unconditional rewriting. Two cases are considered, whether betareduction is allo...

Benzo[a]pyrene (BaP) is potent rodent carcinogen and a reputed human carcinogen. Although much is known about its metabolic activation leading to DNA damage, the mechanisms of its actions are not as well understood at a cellular level. In addressing this, we have established an in vitro model that follows the progression toward neoplastic transformation induced by BaP. The model uses immortal n...

When an IEEE 802.11 ad-hoc network achieves capacity C by using a single channel, the targeted capacity by using two channels should be C  2 . However, most of the multichannel 802.11 protocols proposed in the literature only appear to be able to achieve less than 60% of the C  2 targeted capacity. In our paper [1], we proposed a link-directionality-based dual channel MAC protocol (DCP) to bo...

We give a method to prove confluence of term rewriting systems that contain non-terminating rewrite rules such as commutativity and associativity. Usually, confluence of term rewriting systems containing such rules is proved by treating them as equational term rewriting systems and considering E-critical pairs and/or termination modulo E. In contrast, our method is based solely on usual critica...