12 research outputs found
Decomposition orders : another generalisation of the fundamental theorem of arithmetic
We discuss unique decomposition in partial commutative monoids. Inspired by a result from process theory, we propose the notion of decomposition order for partial commutative monoids, and prove that a partial commutative monoid has unique decomposition iff it can be endowed with a decomposition order. We apply our result to establish that the commutative monoid of weakly normed processes modulo bisimulation definable in ACPe with linear communication, with parallel composition as binary operation, has unique decomposition. We also apply our result to establish that the partial commutative monoid associated with a well-founded commutative residual algebra has unique decompositio
Weak orthogonality implies confluence : the higher-order case
In this paper we prove confluence for weakly orthogonal Higher-Order Rewriting Systems. This generalises all the known `confluence by orthogonality' results
Weak orthogonality implies confluence: the higher-order case
In this paper we prove confluence for weakly orthogonal Higher-Order Rewriting Systems. This generalises all the known `confluence by orthogonality' results
Diagram techniques for confluence
AbstractWe develop diagram techniques for proving confluence in abstract reductions systems. The underlying theory gives a systematic and uniform framework in which a number of known results, widely scattered throughout the literature, can be understood. These results include Newman's lemma, Lemma 3.1 of Winkler and Buchberger, the Hindley–Rosen lemma, the Request lemmas of Staples, the Strong Confluence lemma of Huet, the lemma of De Bruijn
Vicious circles in orthogonal term rewriting systems
In this paper we first study the difference between Weak Normalization (WN) and Strong Normalization (SN), in the framework of first order orthogonal rewriting systems. With the help of the Erasure Lemma we establish a Pumping Lemma, yielding information about exceptional terms, defined as terms that are WN but not SN. A corollary is that if an orthogonal TRS is WN, there are no cyclic reductions in finite reduction graphs. This is a stepping stone towards the insight that orthogonal TRSs with the property WN, do not admit cyclic reductions at all
Iron Behaving Badly: Inappropriate Iron Chelation as a Major Contributor to the Aetiology of Vascular and Other Progressive Inflammatory and Degenerative Diseases
The production of peroxide and superoxide is an inevitable consequence of
aerobic metabolism, and while these particular "reactive oxygen species" (ROSs)
can exhibit a number of biological effects, they are not of themselves
excessively reactive and thus they are not especially damaging at physiological
concentrations. However, their reactions with poorly liganded iron species can
lead to the catalytic production of the very reactive and dangerous hydroxyl
radical, which is exceptionally damaging, and a major cause of chronic
inflammation. We review the considerable and wide-ranging evidence for the
involvement of this combination of (su)peroxide and poorly liganded iron in a
large number of physiological and indeed pathological processes and
inflammatory disorders, especially those involving the progressive degradation
of cellular and organismal performance. These diseases share a great many
similarities and thus might be considered to have a common cause (i.e.
iron-catalysed free radical and especially hydroxyl radical generation). The
studies reviewed include those focused on a series of cardiovascular, metabolic
and neurological diseases, where iron can be found at the sites of plaques and
lesions, as well as studies showing the significance of iron to aging and
longevity. The effective chelation of iron by natural or synthetic ligands is
thus of major physiological (and potentially therapeutic) importance. As
systems properties, we need to recognise that physiological observables have
multiple molecular causes, and studying them in isolation leads to inconsistent
patterns of apparent causality when it is the simultaneous combination of
multiple factors that is responsible. This explains, for instance, the
decidedly mixed effects of antioxidants that have been observed, etc...Comment: 159 pages, including 9 Figs and 2184 reference
Vicious circles in orthogonal term rewriting systems
In this paper we first study the difference between Weak Normalization (WN) and Strong Normalization (SN), in the framework of first order orthogonal rewriting systems. With the help of the Erasure Lemma we establish a Pumping Lemma, yielding information about exceptional terms, defined as terms that are WN but not SN. A corollary is that if an orthogonal TRS is WN, there are no cyclic reductions in finite reduction graphs. This is a stepping stone towards the insight that orthogonal TRSs with the property WN, do not admit cyclic reductions at all