This theory contains a formalization of decreasing diagrams showing that any locally decreasing abstract rewrite system is confluent. We consider the valley (van Oostrom, TCS 1994) and the conversion version (van Oostrom, RTA 2008) and closely follow the original proofs. As an application we prove Newman’s lemma. A description of this formalization is available in [3].

This theory formalizes a commutation version of decreasing diagrams for Church-Rosser modulo. The proof follows Felgenhauer and van Oostrom (RTA 2013). The theory also provides important specializations, in particular van Oostrom’s conversion version (TCS 2008) of decreasing diagrams. We follow the development described in [1]: Conversions are mapped to Greek strings, and we prove that whenever...

We present a connuence criterion, local decreasingness, for abstract reduction systems. This criterion is shown to be a considerable generalisation of several well-known connuence criteria.

Decreasing weight prior distributions for mixture models play an important role in nonparametric Bayesian inference. Various random probability measures with decreasing weights have been previously explored and it has shown that they provide efficient alternative to the more traditional Dirichlet process model. This ordering of implicitly alleviates so-called label switching problem, as larger ...