A reducing automaton (red-automaton) is a deterministic automaton proposed for checking word and sub-word correctness by the use of analysis by reduction. Its monotone version characterizes the class of deterministic context-free languages (DCFL). We propose a method for a construction of a deterministic monotone enhancement of any monotone reducing automaton which is able with the help of spec...

Qualitative models are more suitable than classical quantitative models in many tasks like Model-based Diagnosis (MBD), explaining system behavior, and designing novel devices from first principles. Monotonicity is an important feature to leverage when constructing qualitative models. Detecting monotone pieces robustly and efficiently from sensor or simulation data remains an open problem. This...

In this paper we analyze the iteration-complexity of the hybrid proximal extragradient (HPE) method for finding a zero of a maximal monotone operator recently proposed by Solodov and Svaiter. One of the key points of our analysis is the use of a new termination criteria based on the εenlargement of a maximal monotone operator. The advantages of using this termination criterion it that its defin...

In this paper, we consider the monotone inclusion problem consisting of the sum of a continuous monotone map and a point-to-set maximal monotone operator with a separable two-block structure and introduce a framework of block-decomposition prox-type algorithms for solving it which allows for each one of the single-block proximal subproblems to be solved in an approximate sense. Moreover, by sho...

The chain method of point location was introduced in Lecture 6. This lecture describes the preprocessing required to implement the chain method. It also describes how to transform an arbitrary subdivision of the plane into a subdivision in which all regions are monotone. This allows the chain method to be applied to arbitrary point location problems. Recall that the planar point location proble...

In this paper, we apply our proposed early parallel adaptive computing methodology for numerical solution of semiconductor device equations with triangular meshing technique. This novel simulation based on adaptive triangular mesh, finite volume, monotone iterative, and a posteriori error estimation methods, is developed and successfully implemented on a Linux-cluster with message passing inter...

An evolution equation, arising in the study of the Dynamical Systems Method (DSM) for solving equations with monotone operators, is studied in this paper. The evolution equation is a continuous analog of the regularized Newton method for solving ill-posed problems with monotone nonlinear operators F . Local and global existence of the unique solution to this evolution equation are proved, appar...

The purpose of this article is to prove strong convergence theorems for weak relatively nonexpansive mapping which is firstly presented in this article. In order to get the strong convergence theorems for weak relatively nonexpansive mapping, the monotone CQ iteration method is presented and is used to approximate the fixed point of weak relatively nonexpansive mapping, therefore this article a...

In this work, it is presented iterative schemes for achieving to common points of the solutions set of the system of generalized mixed equilibrium problems, solutions set of the variational inequality for an inverse-strongly monotone operator, common fixed points set of two infinite sequences of relatively nonexpansive mappings and common zero points set of two finite sequences of maximal monot...