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Krasimir Yordzhev

Publications and source records attributed to Krasimir Yordzhev.

At least 37 records · Page 2Linked to original sources
arXiv2014

The assertive profile of the Bulgarian students in computer science and computer engineering

Different points of view on the nature and content of the assertiveness are followed in this paper. The main purpose is to study the assertive profile of Bulgarian students in computer science and computer engineering by analyzing the components of assertiveness. Research was performed using testing methods. It was found that the level of expressivity of this personal quality among subjects were above-average level.

cs.CY↗
arXiv2014

On the probability of two randomly generated S-permutation matrices to be disjoint

The concept of S-permutation matrix is considered in this paper. It defines when two binary matrices are disjoint. For an arbitrary $n^2 \times n^2$ S-permutation matrix, a lower band of the number of all disjoint with it S-permutation matrices is found. A formula for counting a lower band of the number of all disjoint pairs of $n^2 \times n^2$ S-permutation matrices is formulated and proven. As a consequence, a lower band of the probability of two randomly generated S-permutation matrices to be disjoint is found. In particular, a different proof of a known assertion is obtained in the work. The cases when $n=2$ and $n=3$ are discussed in detail.

math.CO↗
arXiv2014

On some numerical characteristics of a bipartite graph

The paper consider an equivalence relation in the set of vertices of a bipartite graph. Some numerical characteristics showing the cardinality of equivalence classes are introduced. A combinatorial identity that is in relationship to these characteristics of the set of all bipartite graphs of the type $g=\langle R_g \cup C_g, E_g \rangle$ is formulated and proved, where $V=R_g \cup C_g$ is the set of vertices, $E_g$ is the set of edges of the graph $g$, $ |R_g |=m\ge 1$, $|C_g |= n\ge 1$, $|E_g |=k\ge 0$, $m,n$ and $k$ are integers.

math.CO↗
arXiv2014

On an Algorithm for Isomorphism-Free Generations of Combinatorial Objects

In the work are defined the concepts semi-canonical and canonical binary matrix. What is described is an algorithm solving the combinatorial problem for finding the semi-canonical matrices in the set Λ_n^k consisting of all n\times n binary matrices having exactly k 1's in every row and every column without perambulating all elements. In the described algorithm bitwise operations are substantially used. In this way it becomes easier to find the solution to the problem for receiving one representative from every equivalence class regarding the introduced in the article equivalence relation in the set Λ_n^k . The last problem is equivalent to the problem for finding all canonical matrices in Λ_n^k .

cs.DS↗
arXiv2014

Fibonacci sequence related to a combinatorial problem on binary matrices

We discuss an equivalence relation on the set of square binary matrices with the same number of 1's in each row and each column. Each binary matrix is represented using ordered n-tuples of natural numbers. We give a few starting values of integer sequences related to the discussed problem. The obtained sequences are new and they are not described in the On-Line Encyclopedia of Integer Sequences (OEIS). We show a relationship between some particular values of the parameters and the Fibonacci sequence.

math.CO↗
arXiv2013

Inclusion of regular and linear languages in group languages

Let $Σ= X\cup X^{-1} = \{ x_1 ,x_2 ,..., x_m ,x_1^{-1} ,x_2^{-1} ,..., x_m^{-1} \}$ and let $G$ be a group with set of generators $Σ$. Let $\mathfrak{L} (G) =\left\{ \left. ω\in Σ^* \; \right\vert \;ω\equiv e \; (\textrm{mod} \; G) \right\} \subseteq Σ^*$ be the group language representing $G$, where $Σ^*$ is a free monoid over $Σ$ and $e$ is the identity in $G$. The problem of determining whether a context-free language is subset of a group language is discussed. Polynomial algorithms are presented for testing whether a regular language, or a linear language is included in a group language. A few finite sets are built, such that each of them is included in the group language $\mathfrak{L} (G)$ if and only if the respective context-free language is included in $\mathfrak{L} (G)$.

cs.FL↗
arXiv2013

Random Permutations, Random Sudoku Matrices and Randomized Algorithms

Some randomized algorithms, used to obtain a random $n^2 \times n^2$ Sudoku matrix, where $n$ is a natural number, is reviewed in this study. Below is described the set $Π_n$ of all $(2n) \times n$ matrices, consisting of elements of the set $\mathbb{Z}_n =\{ 1,2,\ldots ,n\}$, such that every row is a permutation. It is proved that such matrices would be particularly useful in developing efficient algorithms in generating Sudoku matrices. An algorithm to obtain random $Π_n$ matrices is presented in this paper. The algorithms are evaluated according to two criteria - probability evaluation, and time evaluation. This type of criteria is interesting from both theoretical and practical point of view because they are particularly useful in the analysis of computer programs.

math.CO↗
arXiv2013

Some Combinatorial Problems on Binary Matrices in Programming Courses

The study proves the existence of an algorithm to receive all elements of a class of binary matrices without obtaining redundant elements, e. g. without obtaining binary matrices that do not belong to the class. This makes it possible to avoid checking whether each of the objects received possesses the necessary properties. This significantly improves the efficiency of the algorithm in terms of the criterion of time. Certain useful educational effects related to the analysis of such problems in programming classes are also pointed out.

cs.DS↗
arXiv2013

On an Algorithm for Obtaining All Binary Matrices of Special Class Related to V. E. Tarakanov's Formula

An algorithm for obtaining all n\times n binary matrices having exactly 2 units in every row and every column is described in the paper. After analysing the work of the algorithm a formula for calculating the number of these matrices has been obtained. This formula is known and has been obtained using other methods, which by their nature are purely analytical and not constructive. Thus a new, constructive proof of this known formula has been obtained.

cs.DS↗
arXiv2013

The bitwise operations related to a fast sorting algorithm

In the work we discuss the benefit of using bitwise operations in programming. Some interesting examples in this respect have been shown. What is described in detail is an algorithm for sorting an integer array with the substantial use of the bitwise operations. Besides its correctness we strictly prove that the described algorithm works in time O(n). In the work during the realisation of each of the examined algorithms we use the apparatus of the object-oriented programming with the syntax and the semantics of the programming language C++.

cs.PL↗
arXiv2013

A representation of context-free grammars with the help of finite digraphs

For any context-free grammar, we build a transition diagram, that is, a finite directed graph with labeled arcs, which describes the work of the grammar. This approach is new, and it is different from previously known graph models. We define the concept of proper walk in this transition diagram and we prove that a word belongs to a given context-free language if and only if this word can be obtained with the help of a proper walk.

cs.FL↗
arXiv2013

Bitwise operations related to a combinatorial problem on binary matrices

Some techniques for the use of bitwise operations are described in the article. As an example, an open problem of isomorphism-free generations of combinatorial objects is discussed. An equivalence relation on the set of square binary matrices having the same number of units in each row and each column is defined. Each binary matrix is represented using ordered n-tuples of natural numbers. It is shown how by using the bitwise operations can be implemented an algorithm that gets canonical representatives which are extremal elements of equivalence classes relative to a double order on the set of considered objects.

math.CO↗
arXiv2013

Bipartite graphs related to mutually disjoint S-permutation matrices

Some numerical characteristics of bipartite graphs in relation to the problem of finding all disjoint pairs of S-permutation matrices in the general $n^2 \times n^2$ case are discussed in this paper. All bipartite graphs of the type $g= $, where $|R_g |=|C_g |=2$ or $|R_g |=|C_g |=3$ are provided. The cardinality of the sets of mutually disjoint S-permutation matrices in both the $4 \times 4$ and $9 \times 9$ cases are calculated.

math.CO↗
arXiv2012

Computer Administering of the Psychological Investigations: Set-relational Representation

Computer administering of a psychological investigation is the computer representation of the entire procedure of psychological assessments - test construction, test implementation, results evaluation, storage and maintenance of the developed database, its statistical processing, analysis and interpretation. A mathematical description of psychological assessment with the aid of personality tests is discussed in this article. The set theory and the relational algebra are used in this description. A relational model of data, needed to design a computer system for automation of certain psychological assessments is given. Some finite sets and relation on them, which are necessary for creating a personality psychological test, are described. The described model could be used to develop real software for computer administering of any psychological test and there is full automation of the whole process: test construction, test implementation, result evaluation, storage of the developed database, statistical implementation, analysis and interpretation. A software project for computer administering personality psychological tests is suggested.

cs.HC↗
arXiv2012

On Some Entertaining Applications of the Concept of Set in Computer Science Course

Some aspects of programming education are examined in this work. It is emphasised, based on the entertainment value, the most appropriate examples are chosen to demonstrate the different language constructions and data structures. Such an example is the demonstrated algorithm for solving the widespread nowadays "Sudoku" puzzle. This is made, because of the connection with the term set and putting it into practice in the programming. Using the so built program there are solved some combinatorial problems, connected to the Sudoku matrices. Key words: Education in programming, programming languages, data structures, set, Sudoku matrix, Sudoku puzzle.

cs.OH↗
arXiv2012

An Entertaining Example for the Usage of Bitwise Operations in Programming

The present study is meant to fill in some information gaps occurring in the most widespread and well-known educational and reference literature about programming. The stress is laid on a very useful instrument - the bitwise operations, topic which is, unfortunately, seldom dealt with in most of the well-known books on programming. In addition, the research is very useful as regards the topic of overloading operators in any Object-oriented programming course. Given some appropriate examples, with the emphasis being laid on some particular and data structures language constructions, the results are quite interesting. The algorithm of solving the popular Sudoku puzzle is one such entertaining example.

cs.OH↗
arXiv2012

On a Class of Binary Matrices

The paper studies the set of all square binary matrices containing an exact number of 1's in each rows and in each column. A connection is established between the cardinal number of this set and the cardinal number of its subset of matrices containing 1 in the lower right corner. With the help of this result a new proof is advanced of the I. Good and J. Grook theorem. In connection with the firs result a classification has also been made of square binary matrices containing three 1's in each row and column and 1 in the lower right corner.

math.CO↗