2884321
Some remarks on minimal bases and maximal nonbases of integers
Abstract In this note, we generalize the concepts of minimal bases and maximal nonbases for integers, and prove some existence theorems for the generalized minimal bases and maximal nonbases, which generalize some results of Stohr, Deza and Erdos, and Nathanson.
20605726
Extremal Problems in the Construction of Distributed Loop Networks
Let $G(N, A)$ be the Cayley digraph associated with ${\bf Z}/(N)$ and $A$, where $N$ is a positive integer and $A$ is a subset of $\{1, 2, ..., N - 1\}$. Let $N(d, k)$ be the maximum $N$ such that the diameter of $G(N, A)$ is less than or equal to $d$ for some $A = \{a_{1}, a_{2},\ldots, a_{k}\}$ with $1 = a_{1}, < a_{2} < \cdots < a_{k}. An exact formula for $N(d, 2)$ is given, and $N(d, k)$ is estimated for $k \geq 3$. These results provide new bounds for minimal diameter in the construction of loop networks. A relation between this problem and the postage stamp problem in additive number theory is established to enhance the study of these problems.
41488878
On a Network Sensing Problem
Live traffic flow information can help improve the efficiency of a communication network. There are many ways available to monitor the traffic flow of a network. In this paper, we propose a very efficient monitoring strategy. This strategy not only reduces the number of nodes to be monitored but also determines the complete traffic information of the entire network using the information from the monitored nodes. The strategy is optimal for monitoring a network because it reduces the number of monitored nodes to a minimum. Fast algorithms are also presented in this paper to compute the traffic information for the entire network based on the information collected from the monitored nodes. The monitoring scheme discussed in this paper can be applied to the internet, telecommunication networks, wireless ad hoc networks, large scale multiprocessor computing systems, and other information systems where the transmission of information needs to be monitored.
19271257
Extremal Cayley Digraphs of Finite Cyclic Groups
Let $\cay(m,A)$ denote the Cayley digraph on ${\bf Z}_m$ generated by $A$, where ${\bf Z}_m$ is the cyclic group of residues modulo $m$. Let $r(m,A)$ denote the average distance of $\cay(m,A)$. For any $r\ge1$ and $k\ge1$ define $m^*(r,k)$ as the largest positive integer $m$ such that the average distance of the Cayley digraph $\hbox{Cay}(m,A)$ is at most $r$ for some set $A$ with $k$ elements. In this paper, an asymptotic formula for $m^*(r,2)$ is proved and a lower bound for $m^*(r,k)$ is also obtained for $k\ge3$. Applications to the construction of optimal distributed loop networks is discussed in this paper. A lower bound of the average order of subsets for asymptotic bases in number theory is proved using the main theorem of this paper.
40163188
Triple Loop Networks with Minimal Transmission Delay
A multiloop network is a Cayley digraph of the additive group ℤm of integers modulo m generated by a set A of k ≥ 2 "steps". Because of their application to the computer network design, multiloop networks have been studied extensively. Given an integer d ≥ 2 and a real number r > 1, let m(d,3) be the maximum size of a triple loop network with transmission delay (diameter) less than or equal to d, and let m*(r,3) be the maximum size of a triple loop network with average transmission delay less than or equal to r. In this paper, the following lower bounds are proved: which improve earlier lower bounds by Jia and Aguilo, Fiol and Garcia.
13944177
A pragmatic approach to formalizing object-oriented modeling and development
Despite recent developments in formal methods, these methods have yet to enter the mainstream of the software industry. We first examine the pragmatic obstacles to making formal methods practical and usable. Then we present a pragmatic approach to integrate a popular object oriented modeling notation UML and a popular formal notation Z. Our approach is distinctive in its emphasis on overcoming the practical obstacles. We also present a light weight supporting tool for our approach. A prototype of the supporting tool is completed. It allows us to demonstrate the feasibility and capability of our approach.
16675541
The GAPLA: a globally asynchronous locally synchronous FPGA architecture
This paper proposes GAPLA: a globally asynchronous locally synchronous programmable logic array architecture. The whole FPGA area is divided into locally synchronous blocks wrapped with asynchronous I/O interfaces. Data communications between synchronous blocks are controlled by 2-phase handshaking signals. The size and shape of each locally synchronous block are programmable so that different modules in a design can be effectively implemented. Each block could run at higher speed because only the fast local interconnections are used. Experimental results show an up to 28% performance improvement compared to the conventional FPGAs with small area overhead (around 2%).
42148814
Using GALS architecture to reduce the impact of long wire delay on FPGA performance
17179157
Conditional Functional Dependencies for Data Cleaning
We propose a class of constraints, referred to as conditional functional dependencies (CFDs), and study their applications in data cleaning. In contrast to traditional functional dependencies (FDs) that were developed mainly for schema design, CFDs aim at capturing the consistency of data by incorporating bindings of semantic ally related values. For CFDs we provide an inference system analogous to Armstrong's axioms for FDs, as well as consistency analysis. Since CFDs allow data bindings, a large number of individual constraints may hold on a table, complicating detection of constraint violations. We develop techniques for detecting CFD violations in SQL as well as novel techniques for checking multiple constraints in a single query. We experimentally evaluate the performance of our CFD-based methods for inconsistency detection. This not only yields a constraint theory for CFDs but is also a step toward a practical constraint-based method for improving data quality.
2524138
Code synthesis based on object-oriented design models and formal specifications
Presents an approach to synthesizing functional and robust code from object-oriented design models and Z data and operation specifications. The approach used is based on an integrated notation of the Unified Modeling Language (UML) and a slightly extended Z notation to include object-oriented concepts and structures. Our approach generates fully functional code which can be compiled and executed without modifications. The information from object-oriented analysis and design models along with the formal specifications are combined, analyzed and translated into an intermediate representation from which code can be generated. A research prototype has been developed to demonstrate the feasibility and the effectiveness of our approach.