8,884 research outputs found
On the Error Resilience of Ordered Binary Decision Diagrams
Ordered Binary Decision Diagrams (OBDDs) are a data structure that is used in
an increasing number of fields of Computer Science (e.g., logic synthesis,
program verification, data mining, bioinformatics, and data protection) for
representing and manipulating discrete structures and Boolean functions. The
purpose of this paper is to study the error resilience of OBDDs and to design a
resilient version of this data structure, i.e., a self-repairing OBDD. In
particular, we describe some strategies that make reduced ordered OBDDs
resilient to errors in the indexes, that are associated to the input variables,
or in the pointers (i.e., OBDD edges) of the nodes. These strategies exploit
the inherent redundancy of the data structure, as well as the redundancy
introduced by its efficient implementations. The solutions we propose allow the
exact restoring of the original OBDD and are suitable to be applied to
classical software packages for the manipulation of OBDDs currently in use.
Another result of the paper is the definition of a new canonical OBDD model,
called {\em Index-resilient Reduced OBDD}, which guarantees that a node with a
faulty index has a reconstruction cost , where is the number of nodes
with corrupted index
Disparate Statistics
Statistical evidence is crucial throughout disparate impact’s three-stage analysis: during (1) the plaintiff’s prima facie demonstration of a policy’s disparate impact; (2) the defendant’s job-related business necessity defense of the discriminatory policy; and (3) the plaintiff’s demonstration of an alternative policy without the same discriminatory impact. The circuit courts are split on a vital question about the “practical significance” of statistics at Stage 1: Are “small” impacts legally insignificant? For example, is an employment policy that causes a one percent disparate impact an appropriate policy for redress through disparate impact litigation? This circuit split calls for a comprehensive analysis of practical significance testing across disparate impact’s stages. Importantly, courts and commentators use “practical significance” ambiguously between two aspects of practical significance: the magnitude of an effect and confidence in statistical evidence. For example, at Stage 1 courts might ask whether statistical evidence supports a disparate impact (a confidence inquiry) and whether such an impact is large enough to be legally relevant (a magnitude inquiry). Disparate impact’s texts, purposes, and controlling interpretations are consistent with confidence inquires at all three stages, but not magnitude inquiries. Specifically, magnitude inquiries are inappropriate at Stages 1 and 3—there is no discriminatory impact or reduction too small or subtle for the purposes of the disparate impact analysis. Magnitude inquiries are appropriate at Stage 2, when an employer defends a discriminatory policy on the basis of its job-related business necessity
Organization of the channel-switching process in parallel computer systems based on a matrix optical switch
After a classification and analysis of electronic and optoelectronic switching devices, the design principles and structure of a matrix optical switch is described. The switching and pair-exclusion operations in this type of switch are examined, and a method for the optical switching of communication channels is elaborated. Finally, attention is given to the structural organization of a parallel computer system with a matrix optical switch
On reliable computation over larger alphabets
We present two new positive results for reliable computation using formulas
over physical alphabets of size . First, we show that for logical
alphabets of size the threshold for denoising using gates subject to
-ary symmetric noise with error probability is strictly larger
that possible for Boolean computation and we demonstrate a clone of -ary
functions that can be reliably computed up to this threshold. Secondly, we
provide an example where , showing that reliable Boolean computation
can be performed using -input ternary logic gates subject to symmetric
ternary noise of strength by using the additional alphabet
element for error signalling.Comment: 14 pages, 2 figure
Asynchronous logic for high variability nano-CMOS
At the nanoscale level, parameter variations in fabricated devices cause extreme variability in delay. Delay variations are also the main issue in subthreshold operation. Consequently, asynchronous logic seems an ideal, and probably unavoidable choice, for the design of digital circuits in nano CMOS or other emerging technologies. This paper examines the robustness of one particular asynchronous logic: quasi-delay insensitive or QDI. We identify the three components of this logic that can be affected by extreme variability: staticizer, isochronic fork, and rings. We show that staticizers can be eliminated, and isochronic forks and rings can be made arbitrarily robust to timing variations
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