Array-Range Analysis computes at compile time the range of possible index values for each array-index expression in a program. This information can be used to detect potential out-of-bounds array accesses and to identify non-aliasing array accesses. In a language like C, where arrays can be accessed indirectly via pointers, and where pointer arithmetic is allowed, range analysis must be extende...

For a graph G = (V,E) and a binary labeling f : V (G) → Z2, let vf (i) = |f−1(i)|. The labling f is said to be friendly if |vf (1)−vf (0)| ≤ 1. Any vertex labeling f : V (G) → Z2 induces an edge labeling f∗ : E(G) → Z2 defined by f∗(xy) = |f(x)− f(y)|. Let ef (i) = |f∗−1(i)|. The friendly index set of the graph G, denoted by FI(G), is defined by FI(G) = {|ef (1)− ef (0)| : f is a friendly verte...

The compression is a vital field in image processing which reduces the bandwidth during data transfer in multimedia communications. In this paper, we propose Image Compression using Self Organizing Map (SOM) and Discrete Wavelet Transform (DWT) with Error Correction. The input image is considered from standard database and modified to 4x4 blocks and rearranged as 16x4096 input vectors and appli...

In this paper, Symmetric Trapezoidal Intuitionistic Fuzzy Numbers (STIFNs) have been introduced and their desirable properties are also studied. A new type of intuitionistic fuzzy arithmetic operations for STIFN have been proposed based on ( , )   -cuts. A numerical example is considered to elaborate the proposed arithmetic operations. These operations find applications in solving linear prog...

We shall denote the set of all regularly varying functions by R. We shall also denote by L the set of slowly slowly varying (or slowly oscillating) functions, namely those functions in R for which the index ρ = 0. It is easy to show that if h ∈ R, then there exists L ∈ L such that h(x) = xL(x), with ρ being the index of h. Slowly varying functions arise naturally in many branches of number theo...

9] for example, and, in this paper, we introduce an index In this paper we present a rigorous theoretical analysis of the main properties of a double base number system, using bases 2 and 3; in particular we emphasize the sparseness of the representation. A simple geometric interpretation allows an efficient implementation of the basic arithmetic operations and we introduce an index calculus fo...

Using the Arthur-Selberg trace formula we express the index of a Dirac operator on an arithmetic quotient manifold as the integral over the index form plus a sum of orbital integrals. For the Euler operator these orbital integrals are shown to vanish for products of certain rank one spaces. In this case the index theorem looks exactly as in the compact case.

Range analysis is used to optimize circuits and to allocate the bit-width. In this paper we introduce a new and efficient static method to analyze the datapath represented by a polynomial, and compute the range for the datapath, then yield the smallest output bit-width. The method is based on Arithmetic Transform which can guarantee accuracy, and can explore polynomials with single or multiple ...

The purpose is to study the strength of Ramsey’s Theorem for pairs restricted to recursive assignments of k-many colors, with respect to Intuitionistic Heyting Arithmetic. We prove that for every natural number k ≥ 2, Ramsey’s Theorem for pairs and recursive assignments of k colors is equivalent to the Limited Lesser Principle of Omniscience for Σ 3 formulas over Heyting Arithmetic. Alternative...

ÐThis note relates to a recently published partly tutorial article that presents some discussion of the polynomial form of Boolean functions and its applications based on the literature published in English and German. We show that a lot of the research in this area has also been done in Eastern Europe, and this note aims to present these unknown developments. The most recent work in this area ...