This paper presents efficient n-way plurality and threshold voting algorithms based on the type of voting (exact, inexact, or approval), rule for output selection (plurality or threshold) and properties of the input object space (size and structure). Exact voting is the most common voting method and is the easiest to implement. Inexact voting algorithms are more complicated due to intransitivity of approximate equality. In approval voting, each input to the voting process consists of a finite or infinite set of values that have been "approved" by the corresponding computation channel and the value, or set of values, with the highest approval voting must emerge as output. Multiple approved values can result from a nonunique answer to a given problem or from uncertainties in the solution process. For exact voting, the complexity of an n-way voting algorithm depends on the structure of the input object space. Threshold voting often requires less time and space, except when the threshold is very small. The author extends the techniques for designing efficient exact voting algorithms to inexact and approval voting schemes. Results show that optimal linear-time (in n) voting algorithms are available when the input object space is small. Next in the time-complexity hierarchy is the case of a totally-ordered object space that supports worst-case order-[n/spl middot/log(n)]-time algorithms for both exact and inexact voting as well as for certain approval-voting schemes. >

Voting algorithms

How do computers go wrong and what can we do about it? This tutorial outlines the causes of faults and the basic techniques for dealing with them.

Fault-Tolerant Microprocessor-Based Systems

Designs of hardware voters are presented that can be easily pipelined to accommodate extremely high data rates. Design strategies for bit-voters and word-voters are described. Examples of resultant designs are given and each design is evaluated with respect to cost and performance. Both ordinary and generalized m-out-of-n voting, with arbitrary vote assigned to the inputs, are considered. Median voters can be synthesized by simple variants of the design methods. Using currently available technology, these designs can operate at speeds of many millions of votes per second. For majority bit-voters with small values of n, a multiplexer-based design method generally yields the best realizations while for larger values of n, designs based on selection networks tend to be most efficient. For word voters, cost-effective designs based on modified or augmented sorting networks are feasible. In either case, the rich theory developed for the analysis and synthesis of parallel/pipelined sorting networks directly benefits the design process. >

http://ieeexplore.ieee.org/iel1/24/2794/00085461.pdf

Voting networks

Real-time systems are those which must execute all tasks within their timing constraints. Due to the catastrophic consequences of missing deadlines of some realtime tasks, fault tolerance is an essential component of such systems. This thesis introduces techniques to enhance the fault tolerance capability of real-time systems by incorporating time redundancy. Time redundancy is essential in ultrareliable real-time systems where correlated faults must be tolerated. It can also be used to detect and tolerate transient faults, which are a majority of the faults in computing systems. This thesis demonstrates how time redundancy can be used in conjunction with hardware and software redundancy to tolerate a variety of faults in real-time systems. This thesis considers several di erent system and task models, and for each model, presents a schedulability test (a utilization bound or a set of conditions) which guarantees that all tasks in the system will satisfy their timing constraints even in the presence of faults. The thesis studies the tradeo between the fault tolerance capability and resource utilization of the system (which decreases due to the added redundancy). New techniques are introduced to increase the system utilization. Efcient scheduling algorithms and bounds are presented to ensure high schedulability of tasks. The fault tolerance approaches presented in this thesis are thoroughly evaluated. The time after which a system recovers from one fault and is ready to tolerate a second one is measured for static and dynamic systems. Various tradeo studies are conducted to help the system designer make appropriate choices. Extensive simulation results explain the e ects of various input parameters such as task characteristics,

Guaranteeing fault tolerance through scheduling in real-time systems

A fault-tolerant microprocessor system designed to provide digital control for an active magnetic bearing is described. This particular control problem demands significant processing power, is easily divided into relatively independent parallel tasks, and cannot tolerate controller failures. The overall system requirements and architecture are described, as is the design of the digital control module and the analog I/O board. The fault tolerance of the system is evaluated. Extensive computer simulations of system reliability models verified that the design satisfies all of the reliability requirements. Although the system was designed for a specific problem, much effort was expended to make it general enough for applications to a wide range of real-time applications. >

A fault-tolerant multiprocess controller for magnetic bearings

This paper discusses the operation of a chemical reactor and particularly the need for highly reliable instrumentation and control for critical processes. It describes the use of fault tolerance for the computer control to provide a level of reliability previously unachievable with standard computer control systems. The provision of highly reliable interface equipment to the reactor itself is described and approaches are presented for solving the problem of faults in the sensors and actuators. The paper discusses a specific example chemical reactor and the benefits that are achievable using a fault tolerant control computer system.

C. Scott Harclerode

Papers

Programmable Control of a Chemical Reactor Using a Fault Tolerant Computer