Fundamenta Informaticae - Volume 174, issue 2

Authors: Bong, Novi | Bača, Martin | Semaničová-Feňovčíková, Andrea | Sugeng, Kiki A. | Wang, Tao-Ming

Article Type: Research Article

Abstract: We investigate a local face antimagic labeling of plane graphs, and we introduce a new graph characteristic, namely local face antimagic chromatic number of type (a ; b ; c ). Then we determine the precise value of this parameter for wheels and ladders.

Keywords: plane graph, local face antimagic labeling, local face antimagic chromatic number of type (a; b; c)

DOI: 10.3233/FI-2020-1934

Citation: Fundamenta Informaticae, vol. 174, no. 2, pp. 103-119, 2020

Authors: Kaniecki, Mariusz | Kosakowska, Justyna

Article Type: Research Article

Abstract: In the paper we investigate an algorithmic associative binary operation * on the set ℒℛ1 of Littlewood-Richardson tableaux with entries equal to one. We extend * to an algorithmic nonassociative binary operation on the set ℒℛ1 × ℕ and show that it is equivalent to the operation of taking the generic extensions of objects in the category of homomorphisms from semisimple nilpotent linear operators to nilpotent linear operators. Thus we get a combinatorial algorithm computing generic extensions in this category.

Keywords: Littlewood-Richardson tableaux, partitions, invariant subspaces, nilpotent linear operators, generic extensions, pickets, degeneration partial order, combinatorial algorithms

DOI: 10.3233/FI-2020-1935

Citation: Fundamenta Informaticae, vol. 174, no. 2, pp. 121-136, 2020

Authors: Keshavarzian, Nazanin | Borumand Saeid, Arsham | Tehranian, Abolfazl

Article Type: Research Article

Abstract: Hamming codes are of primary concern in information theory and its applications. Despite a number of researches that have been conducted on such codes and their characterizations, dealing with the properties of previously introduced codes in a BCK-algebraic framework has not been considered in earlier works. This paper investigates a code constructed based on BCK-algebraic models and proposes an algorithm corresponding to the presented code. It is noticeable that the suggested rendered algorithm is also established on the basis of the elements of a BCK-algebra. In fact, both the Hamming distance and dimension, associated with the presented code, can be …estimated through a BCK-algebra structure due to the mechanism of its algorithm which is heavily dependent on the parity check matrix. In addition, the way in which the codes are designed contributes substantially to classification of them and to extract greater number of their attributes compared to the previous works. The highlight of the proposed method is that the number of atoms of the BCK-algebra plays a key role in calculation of the Hamming distance and dimension of these codes. Moreover, the obtained codes possess specified and recognizable Hamming distance which are essential in performing error-correcting, error-detecting and decoding tasks. Show more

Keywords: BCI/BCK-algebra, Binary code, linear code, parity check matrix, error-detecting, Hamming distance, incidence structure, BCK-incidence vector, Algorithm, Orthogonal code, Atom, Generator matrix

DOI: 10.3233/FI-2020-1936

Citation: Fundamenta Informaticae, vol. 174, no. 2, pp. 137-165, 2020

Authors: Lin, Yidong | Li, Jinjin | Peng, Liangxue | Feng, Ziqin

Article Type: Research Article

Abstract: Topological base plays a foundational role in topology theory. However, few works have been done to find the minimal base, which would make us difficult to interpret the internal structure of topological spaces. To address this issue, we provide a method to convert the finite topological space into Boolean matrix and some properties of minimal base are investigated. According to the properties, an algorithm(URMB) is proposed. Subsequently, the relationship between topological space and its sub-space with respect to the base is concentrated on by Boolean matrix. Then, a fast algorithm(MMB) is presented, which can avoid a mass of redundant computations. …Finally, some numerical experiments are given to show the advantage and the effectiveness of MMB compared with URMB. Show more

Keywords: Algorithm, Boolean matrix, Finite topology, Minimal base

DOI: 10.3233/FI-2020-1937

Citation: Fundamenta Informaticae, vol. 174, no. 2, pp. 167-183, 2020

Authors: Djordjević, Radosav | Ikodinović, Nebojša | Stojanović, Nenad

Article Type: Research Article

Abstract: The aim of this article is developing a formal system suitable for reasoning about the distance between propositional formulas. We introduce and study a formal language which is the extension of the classical propositional language obtained by adding new binary operators D≤s and D≥s , s ∈ Range, where Range is a fixed finite set. In our language it is allowed to make formulas of the form D≤s (α ; β ) with the intended meaning ’distance between formulas α and β is less than or equal to s ’. The semantics of …the proposed language consists of possible worlds with a distance function defined between sets of worlds. Show more

Keywords: metric operators, soundness, completeness, compactness

DOI: 10.3233/FI-2020-1938

Citation: Fundamenta Informaticae, vol. 174, no. 2, pp. 185-199, 2020