A mathematical framework for algorithm-based fault-tolerant computing over a ring of integers

1994 ◽  
Vol 13 (5) ◽  
pp. 625-653 ◽  
Author(s):  
Hari Krishna
Keyword(s):  
Fault Tolerant ◽  
Mathematical Framework ◽  
Ring Of Integers

Optimizing Fault Tolerance for Multi-Processor System-on-Chip

2011 ◽  
pp. 66-91 ◽  
Author(s):  
Dimitar Nikolov ◽  
Mikael Väyrynen ◽  
Urban Ingelsson ◽  
Virendra Singh ◽  
Erik Larsson
Keyword(s):  
Fault Tolerance ◽  
Error Probability ◽  
Fault Tolerant ◽  
General Purpose ◽  
System On Chip ◽  
Probability Estimation ◽  
Communication Overhead ◽  
Mathematical Framework ◽  
Safety Critical ◽  
On Chip

While the rapid development in semiconductor technologies makes it possible to manufacture integrated circuits (ICs) with multiple processors, so called Multi-Processor System-on-Chip (MPSoC), ICs manufactured in recent semiconductor technologies are becoming increasingly susceptible to transient faults, which enforces fault tolerance. Work on fault tolerance has mainly focused on safety-critical applications; however, the development of semiconductor technologies makes fault tolerance also needed for general-purpose systems. Different from safety-critical systems where meeting hard deadlines is the main requirement, it is for general-purpose systems more important to minimize the average execution time (AET). The contribution of this chapter is two-fold. First, the authors present a mathematical framework for the analysis of AET. Their analysis of AET is performed for voting, rollback recovery with checkpointing (RRC), and the combination of RRC and voting (CRV) where for a given job and soft (transient) error probability, the authors define mathematical formulas for each of the fault-tolerant techniques with the objective to minimize AET while taking bus communication overhead into account. And, for a given number of processors and jobs, the authors define integer linear programming models that minimize AET including communication overhead. Second, as error probability is not known at design time and it can change during operation, they present two techniques, periodic probability estimation (PPE) and aperiodic probability estimation (APE), to estimate the error probability and adjust the fault tolerant scheme while the IC is in operation.

scholarly journals Model-free reconfiguration mechanism for fault tolerance

2012 ◽  
Vol 22 (1) ◽  
pp. 125-137 ◽  
Author(s):  
Tushar Jain ◽  
Joseph Yamé ◽  
Dominique Sauter
Keyword(s):  
Fault Tolerance ◽  
Fault Diagnosis ◽  
Fault Tolerant ◽  
Fault Tolerant Control ◽  
Vantage Point ◽  
Point Of View ◽  
Mathematical Framework ◽  
Tolerance Mechanism ◽  
Fault Accommodation ◽  
Model Free

Model-free reconfiguration mechanism for fault toleranceThe problem of fault tolerant control is studied from the behavioral point of view. In this mathematical framework, the concept of interconnection among the variables describing the system is a key point. The problem is that the behavior we intend to control is not known. Therefore, we are interested in designing a fault accommodation scheme for an unknown behavior through an appropriate behavioral interconnection. Here we deal simply with the trajectories that are generated by the system in real time. These trajectories determine the behavior of a system in various (faulty/healthy) modes. Based on the desired interconnected behavior, only the trajectories that obey certain laws are selected. These laws, representing the desired behavior, can indeed be achieved by a regular interconnection. Thus, when the trajectories do not belong to a certain desired behavior, it is considered to be due to the occurrence of a fault in the system. The vantage point is that the fault tolerant control problem now becomes completely a model-free scheme. Moreover, no explicit fault diagnosis module is required in our approach. The proposed fault tolerance mechanism is illustrated on an aircraft during the landing phase.

LPCD framework: Analytical tool or psychological model?

2018 ◽  
Vol 41 ◽  
Author(s):  
David Danks
Keyword(s):  
Decision Making ◽  
Analytical Tool ◽  
Mathematical Framework ◽  
Bayesian Decision ◽  
Perceptual Decision Making ◽  
Psychological Model ◽  
Psychological Reality ◽  
Psychological Theories ◽  
Target Article ◽  
Bayesian Decision Making

AbstractThe target article uses a mathematical framework derived from Bayesian decision making to demonstrate suboptimal decision making but then attributes psychological reality to the framework components. Rahnev & Denison's (R&D) positive proposal thus risks ignoring plausible psychological theories that could implement complex perceptual decision making. We must be careful not to slide from success with an analytical tool to the reality of the tool components.

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