The divide-and-swap [Formula: see text]-ary [Formula: see text]-cube is a recently proposed variant of the hypercube, denoted by [Formula: see text]. It has a smaller diameter and better connectivity than the hypercube. Connectivity and super connectivity are two important parameters for measuring the fault tolerance of interconnection networks. In this work, we obtain the connectivity and super connectivity of the divide-and-swap [Formula: see text]-ary [Formula: see text]-cube.
Parallel contextual array insertion deletion P system (PCAIDPS) generating 2D rectangular picture languages, introduced in 2017, has more generating capacity than the other picture language generating devices like tiling systems and context-sensitive matrix grammars etc. In 2024 another interesting device called pure 2D Eilenberg P system (P2DEPS) based on pure 2D context-free grammars has been studied. In this paper, we compare the generative powers of these two P systems PCAIDPS and P2DEPS.
With the rapid expansion of data centers driven by big data processing and artificial intelligence, the urgent need is to seek and optimize multiprocessor systems based on interconnection networks with high reliability and strong fault tolerability. The generalized K-4-hypercube H-n(4), one extended topology derived from the hypercube, is an ideal candidate for the choice of recursive interconnection networks. To quantitatively evaluate its link fault tolerance under multi-component partition scenarios, this paper investigates the (r+1)-component edge-connectivity of H-n(4). This work provides a precise quantitative metric for evaluating the structural robustness of the generalized K-4-hypercube H-n(4) with a large number of link failures.
Graph entropy is originated from Shannon entropy, which is used to quantify the complexity and uncertainty of networks and is widely applied in fields such as information theory, communication theory and statistics. As a kind of classical graph entropy, the chromatic entropy of a graph plays a key role in describing the structures of networks. Generally, a hypergraph is the extension of a graph, which is often used in characterising complex systems. In this paper, we investigate the chromatic entropy of linear p-uniform unicyclic hypergraphs based on strong vertex coloring. We determine the hypergraphs that attain the maximum and minimum chromatic entropy within this class. Using edge-moving operations, we characterize the extremal structures and derive explicit formulas for their entropy values.
Connectivity is a vital parameter to measure the reliability and fault tolerability of the multiprocessor systems. To better characterize system reliability of resisting the block-based attacks, some structural connectivities have been proposed successively. In this paper, we propose a novel kind of structural connectivity based the cyclic fault pattern, called cyclic fault-block connectivity. Let G be a connected graph and F subset of V(G). Then F is called a cyclic fault-block cut of G if G-F is disconnected so that at least two components of G-F contain cycles and G[F] is connected. The minimum cardinality over all cyclic fault-block cuts of G is called cyclic fault-block connectivity of G, denoted by kappa (c)(FB)(G). Furthermore, we show that the cyclic fault-block connectivity of Q(n )is kappa (c)(FB)(Q(n))=5n-11 for n >= 9.
In this paper, I introduce a novel paradigm called grey automata that integrates grey system theory with classical automata theory to model systems marked by uncertainty and incomplete information. I define grey automata by incorporating grey numbers interval based representations of uncertainty into state transitions, thus extending the conventional finite automata model. I establish the theoretical foundations of grey automata, demonstrating key properties such as closure under union, determinization, state equivalence, and minimality. Furthermore, I provide practical examples, including models for traffic light systems and vending machines, to illustrate the relevance and applicability of our approach in various real-world scenarios.
A cyclic Gray code is an ordered sequence that contains all binary strings of a given length in which each consecutive string differs from the previous one in exactly one coordinate. Such a sequence directly represents a Hamiltonian cycle and path in the hypercube. Ruskey and Savage asked whether every matching in the hypercube extends to a Hamiltonian cycle, and Fink proved that every perfect matching in Qn extends to a Hamiltonian cycle. In this study, we address a problem related to Hamiltonian paths. We prove that every matching at most in five directions where every 4-cycle contains at least one unsaturated vertex, can be extended to a Hamiltonian path joining two vertices in distinct partite sets of Qn, for n >= 5. The only forbidden configurations are the so-called half-layers, which form certain natural obstacles.
The H-P sort is a known algorithm for integer sorting using histogram computation and prefix sum calculation. In this paper, first, by implementing a naive GPU version of H-P sort, we demonstrate that it outperforms the fastest standard library (CUB sort) when the input data range is small compared to the input size. Next, by improving the histogram and prefix-sum algorithms, the optimized algorithm becomes faster than the naive version and, in some aspects where the H-P sort had previously been inferior to the CUB sort, it now outperforms.
With the rapid development of wireless communication networks, the frequency assignment problem for wireless networks has been transformed into a graph labeling problem: specifically, each base station is represented by a vertex in an undirected graph, and vertices that may cause interference are connected by edges, with adjacent vertices unable to use the same frequency. However, determining the frequency assignment for an arbitrary graph is an NP-hard problem. Therefore, based on an exploration of grid network models, this paper focuses on the labeling problem of the cylindrical gird network with fan subgraph model F-m,F-n where m >= 2 and n >= 3, that is, the Cartesian product of the m-order fan graph and the n-order cycle. First, we present lower bounds of radio labeling and several results for this class of network models. Second, we label the vertices of this special graph and determine the optimal number. Finally, through numerical comparisons and application examples, experimental data demonstrate that compared to existing Cartesian product models of cycle and cycle, complete graph and cycle, the topological model designed in this paper has higher optimization under the same number of vertices. Specifically, the Cartesian product model of the fan graph and cycle requires fewer radio labelings.
Recursive algorithms for computing the Frobenius norm of a real array are proposed, based on hypot, a hypotenuse function. Comparing their relative accuracy bounds with those of the BLAS routine DNRM2 it is shown that the proposed algorithms could in many cases be significantly more accurate. The scalar recursive algorithms are vectorized with the Intel's vector instructions to achieve performance comparable to DNRM2, and are further parallelized with OpenCilk. Some scalar algorithms are unconditionally bitwise reproducible, while the reproducibility of the vector ones depends on the vector width. A modification of the proposed algorithms to compute the vector p-norm is also presented.
Quantum games extend classical game theory into the quantum realm by incorporating quantum players and quantum strategies. Two-player quantum games have been widely studied and applied, among other areas, in optimization and decision-making. In this work, we introduce, formalize and analyze a novel class of three-player quantum games, referred to as Proxy Quantum Games (PQGs). In this setting, one player, the Controller, influences or governs the strategic operations executed by a second player, the Proxy, who, in turn, competes directly against a third player, the Opponent. The strategic influence is implemented via controlled unitary operations, whereby the Proxy's available strategies are conditioned on the Controller's quantum state. We further generalize the PQG framework by incorporating multiple Controllers acting on a common Proxy, thereby enabling the study of higher-order strategic interactions and multi-agent influence structures. The objective under consideration is the maximization of the Controller's expected payoff, under various configurations of strategic control and entanglement. Comparative analyses are conducted between the PQG formulation and conventional multiplayer quantum games, highlighting key differences in strategic behavior and payoff distributions.
The strong product serves as an essential method to build parallel processing network models utilizing a number of small graphs. The network models constructed through the strong product incorporate these small graphs as subgraphs and preserve many of the advantageous properties of the factor graphs. The k-distant Hamiltonian walk indicates a generalization of the Hamiltonian cycle, and the k-distant Hamiltonian walk in the graph demonstrates a cyclic sequence of all its vertices, where the distance between two consecutive vertices is k. In the design of wireless sensor networks, the k-distant Hamiltonian walk plays an important role. In this paper, sufficient conditions are determined for the existence of k-distant Hamiltonian walks in the strong product of simple, connected, undirected graphs. These conditions are derived on the basis of the connectivity, degree, and specific edge connectivity of the graph. The existence of k-distant Hamiltonian walks is tested by exploring the strong product topology, with relevant theorems and examples provided, and corresponding algorithms given to verify the applicability and effectiveness of the parallel network model proposed in this paper.
A barrel shifter is a digital circuit used to shift the data word by predetermining the number of bits in a single clock. Typically, the multiplexers are connected in sequence to perform shifting operations. The output of one multiplexer is connected to the input of another multiplexer according to the chosen shift distance. The total number of multiplexers required for implementation is determined by equation nlog2(n). In this paper, an area-minimised barrel shifter is proposed, which reduces the number of multiplexers by (n-1). These reduced multiplexers are replaced by a NOT-AND gate. The proposed design is modelled using Verilog and synthesised in the Xilinx Vivado suite. MOS transistor implementation is verified in Microwind and DSCH tool. Experimental results show that the design is properly working and reduces the transistor count by 19.17%. The proposed design is best suited for area-constraint implementations.
This paper discusses the practical aspects of developing system interfaces for the reliable sensing of the analog resistive state of memristive devices, implementing multi-level resistive memory (ReRAM) cells or synaptic weights in neuromorphic computing applications. More specifically, it presents a general implementation method for ad-hoc sensing systems designed for memristive devices, with a particular focus on the design of the READ circuit module. Through detailed comparison and analysis of experimental results, this study proposes a versatile circuit that utilizes a current-to-voltage converting stage with a transimpedance amplifier (TIA), along with a suggested algorithm for iterative operation which will improve resolution, when needed, at the cost of longer READ processes. The proposed algorithm automatically adjusts the circuit parameters to maintain the output voltage of the TIA within an acceptable range, ensuring high-precision READings. This approach avoids saturation of the TIA while also preventing the low-level signals, which could compromise the precision of the READ process. Simulation results using LTSpice validate the operation and usefulness of the proposed circuit, enhancing the tutorial value of this work for both the practical implementation of research prototypes and more advanced applications of memristive devices developed by students, researchers, and engineers working in emerging device technologies.
Diagnosis plays an important role in measuring the reliability of interconnection networks, and the diagnosability of interconnection networks has been widely investigated. In 2012, Peng et al. proposed the g-good-neighbor diagnosability, which requires that every fault-free processor contains at least g fault-free neighbors. In this paper, we show that the g-good-neighbor diagnosability of folded hypercube-like networks under the PMC model and MM* model when g = 1.
Considering the mutual influence of product prices in adjacent regions on demand, in this paper, we develop a differential game model of transboundary pollution that incorporates emission reduction technologies. By applying optimal control theory, we derive the optimal strategies and pollution stock emission paths for two regions in both non-cooperative and cooperative game scenarios. A comparative analysis of the optimal results and an examination of parameter impacts are conducted for these two scenarios. The research results demonstrate that under cooperative game theory, product prices are lower, optimal production is higher, pollution levels in the air are lower, and social welfare is higher. Furthermore, as price competition intensifies, product prices exhibit a downward trend, while pollution stocks have increased accordingly. Conversely, advancements in emission reduction technology lead to increased regional benefits and a corresponding decrease in pollution stocks.
Connectivity is an important metric for fault tolerance in interconnection networks. Menger’s theorem reveals the relationship between connectivity and disjoint paths in a graph. Disjoint paths not only avoid communication bottlenecks, but also provide alternative paths in case of vertex failures. Let [Formula: see text] [Formula: see text] be a [Formula: see text]-dimensional sub-bubble-sort star of [Formula: see text]. In this paper, we show that [Formula: see text] is strongly Menger (edge) connected. Later, we show that the connectivity and edge-connectivity of [Formula: see text] are uniformly [Formula: see text]. In addition, we show that the 1-extra connectivity of [Formula: see text] is [Formula: see text] for [Formula: see text].
Partial differential equations and systems with certain boundary conditions specify continuous processes significant for both large-scale simulations in computer-aided design using HPC and subsequent real-time control of embedded applications using dedicated hardware. The paper develops a spectrum of techniques based on a family of place-transition nets aimed at the computing and communication structure design for fast mass-parallel numerical solving of PDEs. For the HPC domain, we develop models of interconnects in the form of infinite nets and graphical programs in the form of Sleptsov nets. For the embedded control domain, we develop specialized lattices for fast numerical solving PDE based on integer number approximation specified with Sleptsov-Salwicki nets to be implemented on dedicated hardware, which we prototype on FPGAs. For mass-parallel solving of PDEs, we employ ad-hoc finite-difference schemes and iteration methods that allow us to recalculate the lattice values in a single time cycle suitable for control of hypersonic objects and thermonuclear reactions.
The Hamiltonian problem is a fundamental research topic in graph theory. In this paper, we study a relaxation of the Hamiltonian problem. A graph [Formula: see text] is spanning [Formula: see text]-edge-cyclable if, for any [Formula: see text] independent edges [Formula: see text] of [Formula: see text], there exist [Formula: see text] vertex-disjoint cycles [Formula: see text] in [Formula: see text] such that [Formula: see text] and [Formula: see text] for all [Formula: see text]. Clearly, a graph [Formula: see text] is Hamiltonian if it is spanning [Formula: see text]-edge-cyclable. We focus on spanning [Formula: see text]-edge-cyclability of enhanced hypercube network, which is an important variant of well known hypercube. We prove that the [Formula: see text]-dimensional enhanced hypercube [Formula: see text] is spanning [Formula: see text]-edge-cyclable for [Formula: see text], [Formula: see text] and odd [Formula: see text].
Cyclic codes are a subclass of linear codes. They have efficient encoding and decoding algorithms, so they are used for consumer electronics, data storage systems,and communication systems. In this paper, a class of three-weight cyclic codes over GF(2) whose duals have two zeros is presented. The weight distribution of this class of cyclic codes is settled by quadratic form theory.
