In computer science, a Binary decision diagram is a data structure that is used to represent a Boolean function and to consider a compressed representation of relations. This paper considers the notation of T.B.T (total Binary truth table), and introduces a novel concept of Binary decision (hyper)tree and Binary decision (hyper)diagram, directly and in as little time as possible, unlike previous methods. This study proves that every T.B.T corresponds to a Binary decision (hyper)tree via minimum Boolean expression and presents some conditions on any given T.B.T for isomorphic Binary decision (hyper)trees. Finally, for faster calculations and more complex functions, we offer an algorithm and so Python programming codes such that for any given T.B.T, it introduces a Binary decision (hyper)tree.

Elimination of redundancies in the memory representation is necessary for fast and efficient analysis of large sets of fuzzy data. In this work, we use MTBDDs as the underlying data-structure to represent fuzzy sets and Binary fuzzy relations. This leads to elimination of redundancies in the representation, less computations, and faster analyses. We also extended a BDD package (BuDDy) to support MTBDDs in general and fuzzy sets and relations in particular. Representation and manipulation of MTBDD based fuzzy sets and Binary fuzzy relations are described in this paper. These include design and implementation of different fuzzy operations such as max, min and max-min composition. In particular, an efficient algorithm for computing max-min composition is presented. Effectiveness of our MTBDD based implementation is shown by applying it on fuzzy connectedness and image segmentation problem. Compared to a base implementation, the running time of the MTBDD based implementation was faster (in our test cases) by a factor ranging from 2 to 27. Also, when the MTBDD based data-structure was employed, the memory needed to represent the final results was improved by a factor ranging from 37.9 to 265.5. We also describe our base implementation which is based on matrices.

This article shows that any type of Binary data can be defined as a collection from codewords of variable length. This feature helps us to define an Injective and surjective function from the suggested codewords to the required codewords. Therefore, by replacing the new codewords, the Binary data becomes another Binary data regarding the intended goals. One of these goals is to reduce data size. It means that instead of the original codewords of each Binary data, it replaced the Huffman codewords to reduce the data size. One of the features of this method is the result of positive compression for any type of Binary data, that is, regardless of the size of the code table, the difference between the original data size and the data size after compression will be greater than or equal to zero. Another important and practical feature of this method is the use of symmetric codewords instead of the suggested codewords in order to create symmetry, reversibility and error resistance properties with two-way decoding.

Binary decision Diagram (in short BDD) is an efficient data structure which has been used widely in computer science and engineering. BDD-based attack in key stream cryptanalysis is one of the best forms of attack in its category. In this paper, we propose a new key stream attack which is based on ZDD (Zero-suppressed BDD). We show how a ZDD-based key stream attack is more efficient in time and space complexity over its BDD-based variant against the E0 type of the Bluetooth security mechanism. We implemented it by using the CUDD - Colorado University decision Diagram package. Experimental results show great improvements. We have also derived a mathematical proof, which shows that it is better than the BDDbased attack method even for the worst case analysis.

In this article, first we define a Kripke semantics for normal modal Logic with a Binary operator and we introduce a system K^2 which is sound and complete for this semantics. Then, we will introduce two translations and show that Binary normal modal logic K^2, and unary normal modal logic K, i.e. modal logic with one Binary operator, are very closely related by these two translations. We call a translation a faithful interpretation if provability is preserved in both directions. So, with this terminology we will show that these two translations are faithful interpretation of K into K^2 and vice versa. A logic extending K will be a set of formulas containing K closed under its rules and uniform substitution. A logic extending K^2 is similarly defined. Finally, we will prove that the classes of logics extending K and K^2 are closely related as well and there is a 1-1-correspondence between the logics extending K and extending K^2.

In this paper, we combine two Binary operations ℾ,-Extension and element split-ting under special conditions, to extend Binary matroids. For a given Binary matroid M, we call a matroid obtained in this way a Λ,-Extension of M. We note some attractive properties of this matroid operation, particularly constructing a chordal matroid from a chordal Binary matroid.