Extra Connectivity of Strong Product of Graphs

The $g$-$extra$ $connectivity$ $\kappa_{g}(G)$ of a connected graph $G$ is the minimum cardinality of a set of vertices, if it exists, whose deletion makes $G$ disconnected and leaves each remaining component with more than $g$ vertices, where $g$ is a non-negative integer. The $strong$ $product$ $G_1 \boxtimes G_2$ of graphs $G_1$ and $G_2$ is the graph with vertex set $V(G_1 \boxtimes G_2)=V(G_1)\times V(G_2)$, where two distinct vertices $(x_{1}, y_{1}),(x_{2}, y_{2}) \in V(G_1)\times V(G_2)$ are adjacent in $G_1 \boxtimes G_2$ if and only if $x_{1}=x_{2}$ and $y_{1} y_{2} \in E(G_2)$ or $y_{1}=y_{2}$ and $x_{1} x_{2} \in E(G_1)$ or $x_{1} x_{2} \in E(G_1)$ and $y_{1} y_{2} \in E(G_2)$. In this paper, we give the $g\ (\leq 3)$-$extra$ $connectivity$ of $G_1\boxtimes G_2$, where $G_i$ is a maximally connected $k_i\ (\geq 2)$-regular graph for $i=1,2$. As a byproduct, we get $g\ (\leq 3)$-$extra$ conditional fault-diagnosability of $G_1\boxtimes G_2$ under $PMC$ model

Theory of reliable systems

The analysis and design of reliable systems are discussed. The attributes of system reliability studied are fault tolerance, diagnosability, and reconfigurability. Objectives of the study include: to determine properties of system structure that are conducive to a particular attribute; to determine methods for obtaining reliable realizations of a given system; and to determine how properties of system behavior relate to the complexity of fault tolerant realizations. A list of 34 references is included

Random induced subgraphs of Cayley graphs induced by transpositions

In this paper we study random induced subgraphs of Cayley graphs of the symmetric group induced by an arbitrary minimal generating set of transpositions. A random induced subgraph of this Cayley graph is obtained by selecting permutations with independent probability, $\lambda_n$. Our main result is that for any minimal generating set of transpositions, for probabilities $\lambda_n=\frac{1+\epsilon_n}{n-1}$ where $n^{-{1/3}+\delta}\le \epsilon_n0$, a random induced subgraph has a.s. a unique largest component of size $\wp(\epsilon_n)\frac{1+\epsilon_n}{n-1}n!$, where $\wp(\epsilon_n)$ is the survival probability of a specific branching process.Comment: 18 pages, 1 figur

Assessing the Effectiveness of Defect Prediction-based Test Suites at Localizing Faults

Debugging a software program constitutes a significant and laborious task for programmers, often consuming a substantial amount of time. The need to identify faulty lines of code further compounds this challenge, leading to decreased overall productivity. Consequently, the development of automated tools for fault detection becomes imperative to streamline the debugging process and enhance programmer productivity. In recent years, the field of automatic test generation has witnessed remarkable advancements, significantly improving the efficacy of automatic tests in detecting faults. The localization of faults can be further optimized through the utilization of such sophisticated tools. This dissertation aims to conduct an experimental study that assembles specialized automatic test generation tools designed to detect faults by estimating the likelihood of code being faulty. These tools will be compared against each other to discern their relative performance and effectiveness. Additionally, the study will comprehensively compare developer-generated tests with automatically generated tests to evaluate their respective aptitude for fault detection. Through this investigation, we seek to identify the most effective automated test generation tool while providing valuable insights into the relative merits of developer-generated and automatically generated tests for fault detection

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Tools and Algorithms for the Construction and Analysis of Systems

This open access book constitutes the proceedings of the 28th International Conference on Tools and Algorithms for the Construction and Analysis of Systems, TACAS 2022, which was held during April 2-7, 2022, in Munich, Germany, as part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2022. The 46 full papers and 4 short papers presented in this volume were carefully reviewed and selected from 159 submissions. The proceedings also contain 16 tool papers of the affiliated competition SV-Comp and 1 paper consisting of the competition report. TACAS is a forum for researchers, developers, and users interested in rigorously based tools and algorithms for the construction and analysis of systems. The conference aims to bridge the gaps between different communities with this common interest and to support them in their quest to improve the utility, reliability, exibility, and efficiency of tools and algorithms for building computer-controlled systems

Relating Diagnosability, Strong Diagnosability and Conditional Diagnosability of Strong Networks

An interconnection network\u27s diagnosability is an important measure of its self-diagnostic capability. Based on the classical notion of diagnosability, strong diagnosability and conditional diagnosability were proposed later to better reflect the networks\u27 self-diagnostic capability under more realistic assumptions. In this paper, we study a class of interconnection networks called strong networks, which are n -regular, (n - 1) -connected, and with cn -number no more than n - 3. We build a relationship among the three diagnosability measures for strong networks. Under both PMC and MM* models, given a strong network G with diagnosability t , we prove that G is strongly t -diagnosable if and only if G \u27s conditional diagnosability is greater than t. A simple check can show that almost all well-known regular interconnection networks are strong networks. The significance of this paper\u27s result is that it reveals an important relationship between strong and conditional diagnosabilities, and the proof of strong diagnosability for many interconnection networks under MM* or PMC model is not necessary if their conditional diagnosability can be shown to be strictly larger than their diagnosability

Advances in Robotics, Automation and Control

The book presents an excellent overview of the recent developments in the different areas of Robotics, Automation and Control. Through its 24 chapters, this book presents topics related to control and robot design; it also introduces new mathematical tools and techniques devoted to improve the system modeling and control. An important point is the use of rational agents and heuristic techniques to cope with the computational complexity required for controlling complex systems. Through this book, we also find navigation and vision algorithms, automatic handwritten comprehension and speech recognition systems that will be included in the next generation of productive systems developed by man