This paper discusses the linear complexity property of binary sequences generated using matrix recurrence relation defined over Z4. Generally algorithm to generate random number is based on recursion with seed value/values. In this paper a linear recursion sequence of matrices or vectors over Z4 is generated from which random binary sequence is obtained. It is shown that such sequences have lar...

The Hamming weight of the non-adjacent form is studied in relation to the Hamming weight of the standard binary expansion. In particular, we investigate the expected Hamming weight of the NAF of a n-digit binary expansion with k ones where k is either fixed or proportional to n. The expected Hamming weight of NAFs of binary expansions with large (≥ n/2) Hamming weight is studied. Finally, the c...

The Hamming weight of the non-adjacent form is studied in relation to the Hamming weight of the standard binary expansion. In particular, we investigate the expected Hamming weight of the NAF of a n-digit binary expansion with k ones where k is either fixed or proportional to n. The expected Hamming weight of NAFs of binary expansions with large (≥ n/2) Hamming weight is studied. Finally, the c...

In this work we describe a large new sample of contact binary stars extracted in a uniformmanner from sky patrol data taken by theROTSE-I telescope. ExtensiveROTSE-I light-curve data are combinedwith J-,H-, andK-band near-infrared data taken from theTwoMicronAll Sky Survey to add color information. Contact binary candidates are selected using the observed period-color relation. Candidates are c...

This paper studies the outcome of the amendment voting procedure based on a potentially incomplete binary relation. We assume that the decision-maker evaluates candidates in a list and iteratively updates her choice by comparing the status-quo to the next candidate. With a complete binary relation, it is known that the final selected candidate belongs to the “top cycle.” In reality however, not...

This paper studies the concepts of definability and canonicity in Boolean logic with a binary relation. Firstly, it provides formulas defining first-order or second-order conditions on frames. Secondly, it proves that all formulas corresponding to compatible first-order conditions on frames are canonical.

The basic concept of the fuzzy matrix theory is very simple and can be applied to social and natural situations. A branch of fuzzy matrix theory uses algorithms and algebra to analyse data. It is used by social scientists to analyse interactions between actors and can be used to complement analyses carried out using game theory or other analytical tools. The concepts of fuzzy matrix have been d...

Let (L;C ) be the (up to isomorphism unique) countable homogeneous structure carrying a binary branching C-relation. We study the reducts of (L;C ), i.e., the structures with domain L that are first-order definable in (L;C ). We show that up to existential interdefinability, there are finitely many such reducts. This implies that there are finitely many reducts up to first-order interdefinabili...

In this paper, some important issues of granularity are discussed mainly in information systems (ISs) based on binary relation. Firstly, the vector representation method of knowledge granules is proposed in an information system based on binary relation to eliminate limitations of set representation method. Secondly, operators among knowledge granularity are introduced and some important proper...

Decision theory considers how best to make decisions in the light of uncertainty about data. There are several methodologies that may be used to determine the best decision. In rough set theory, the classification of objects according to approximation operators can be fitted into the Bayesian decision-theoretic model, with respect to three regions (positive, negative, and boundary region). Gran...