On efficient reduction algorithms for some trace rewriting systems

Author(s):  
Michael Bertol ◽  
Volker Diekert
2021 ◽  
pp. 088532822110134
Author(s):  
Sushant Singh ◽  
Udit Kumar ◽  
David Gittess ◽  
Tamil S Sakthivel ◽  
Balaashwin Babu ◽  
...  

Many studies have linked reactive oxygen species (ROS) to various diseases. Biomedical research has therefore sought a way to control and regulate ROS produced in biological systems. In recent years, cerium oxide nanoparticles (nanoceria, CNPs) have been pursued due to their ability to act as regenerative ROS scavengers. In particular, they are shown to have either superoxide dismutase (SOD) or catalase mimetic (CAT) potential depending on the ratio of Ce3+/Ce4+ valence states. Moreover, it has been demonstrated that SOD mimetic activity can be diminished by the presence of phosphate, which can be a problem given that many biological systems operate in a phosphate-rich environment. Herein, we report a CNP formulation with both SOD and catalase mimetic activity that is preserved in a phosphate-rich media. Characterization demonstrated a highly dispersed, stable solution of uniform-sized, spherical-elliptical shaped CNP of 12 ± 2 nm, as determined through dynamic light scattering, zeta potential, and transmission electron microscopy. Mixed valence states of Ce ions were observed via UV/Visible spectroscopy and XPS (Ce3+/Ce4+ > 1) (Ce3+∼ 62%). X-ray diffraction and XPS confirmed the presence of oxygen-deficient cerium oxide (CeO2-x) particles. Finally, the CNP demonstrated very good biocompatibility and efficient reduction of hydrogen peroxide under in-vitro conditions.


1982 ◽  
Vol 5 (3-4) ◽  
pp. 279-299
Author(s):  
Alberto Pettorossi

In this paper we consider combinators as tree transducers: this approach is based on the one-to-one correspondence between terms of Combinatory Logic and trees, and on the fact that combinators may be considered as transformers of terms. Since combinators are terms themselves, we will deal with trees as objects to be transformed and tree transformers as well. Methods for defining and studying tree rewriting systems inside Combinatory Weak Reduction Systems and Weak Combinatory Logic are also analyzed and particular attention is devoted to the problem of finiteness and infinity of the generated tree languages (here defined). This implies the study of the termination of the rewriting process (i.e. reduction) for combinators.


2021 ◽  
Vol 178 (3) ◽  
pp. 173-185
Author(s):  
Arthur Adinayev ◽  
Itamar Stein

In this paper, we study a certain case of a subgraph isomorphism problem. We consider the Hasse diagram of the lattice Mk (the unique lattice with k + 2 elements and one anti-chain of length k) and find the maximal k for which it is isomorphic to a subgraph of the reduction graph of a given one-rule string rewriting system. We obtain a complete characterization for this problem and show that there is a dichotomy. There are one-rule string rewriting systems for which the maximal such k is 2 and there are cases where there is no maximum. No other intermediate option is possible.


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