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CVT and XOR are two binary operations together used to calculate the sum of two non-negative integers on using a recursive mechanism. In this present study the convergence behaviors of this recursive mechanism has been captured through a tree like structure named as CVT-XOR Tree. We have analyzed how to identify the parent nodes, leaf nodes and internal nodes in the CVT-XOR Tree. We also provide the parent information, depth information and the number of children of a node in different CVT-XOR Trees on defining three different matrices. Lastly, one observation is made towards very old Mathematical problem of Goldbach Conjecture.
In this paper the theory of Carry Value Transformation (CVT) is designed and developed on a pair of n-bit strings and is used to produce many interesting patterns. One of them is found to be a self-similar fractal whose dimension is same as the dimen
The notion of Carry Value Transformation (CVT) is a model of Discrete Deterministic Dynamical System. In this paper, we have studied some interesting properties of CVT and proved that (1) the addition of any two non-negative integers is same as the s
Carry Value Transformation (CVT) is a model of discrete dynamical system which is one special case of Integral Value Transformations (IVTs). Earlier in [5] it has been proved that sum of two non-negative integers is equal to the sum of their CVT and
The canonical tree-decomposition theorem, given by Robertson and Seymour in their seminal graph minors series, turns out to be one of the most important tool in structural and algorithmic graph theory. In this paper, we provide the canonical tree dec
In the study of extensions of polytopes of combinatorial optimization problems, a notorious open question is that for the size of the smallest extended formulation of the Minimum Spanning Tree problem on a complete graph with $n$ nodes. The best know