Energy Bounds for Fault-Tolerant Nanoscale Designs

Diana Marculescu

Home/Archive/arXiv

arXiv · 0710.4680

Energy Bounds for Fault-Tolerant Nanoscale Designs

Diana Marculescu

View original source ↗Read source document ↗Export metadata ↓

Abstract

The problem of determining lower bounds for the energy cost of a given nanoscale design is addressed via a complexity theory-based approach. This paper provides a theoretical framework that is able to assess the trade-offs existing in nanoscale designs between the amount of redundancy needed for a given level of resilience to errors and the associated energy cost. Circuit size, logic depth and error resilience are analyzed and brought together in a theoretical framework that can be seamlessly integrated with automated synthesis tools and can guide the design process of nanoscale systems comprised of failure prone devices. The impact of redundancy addition on the switching energy and its relationship with leakage energy is modeled in detail. Results show that 99% error resilience is possible for fault-tolerant designs, but at the expense of at least 40% more energy if individual gates fail independently with probability of 1%.

Explore related subjects

cs.CC cs.IT math.IT

Keep this discovery

BibTeX RIS

Diana Marculescu. 2007-10-25. Energy Bounds for Fault-Tolerant Nanoscale Designs. https://arxiv.org/abs/0710.4680

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Computational Complexity of Holant Problems on 4-regular Graphs from the Stable Subgroup Sequence of $SL(2,\mathbb{C})$

The Holant framework provides a general setting for studying counting problems and includes graph homomorphisms (\#GH) and counting constraint satisfaction problems (\#CSP) as special cases. Over the past twenty years, a series of computational complexity dichotomies have been established for Holant problems, but the classification for complex-valued signatures is still open. The main obstacle is the case in which all signatures have even arity. In this paper, we establish a dichotomy for Holant problems with a complex-valued 4-ary signature, which is a key base case for the full classification of Holant problems. We present a new strategy by introducing Schur's theorem, the classification of finite subgroups of $\mathrm{SL}(2,\mathbb{C})$ and stable subgroup sequences into the proof. These new techniques are of independent interest.

cs.CC↗

arXiv2026

Max Independent Set Remains NP-hard when Excluding a Planar Induced Minor

We show that there is a fixed planar graph $H$, namely the $5 \times 5$ grid, such that Max Independent Set remains NP-hard in $H$-induced-minor-free graphs. This refutes the Dallard--Milani\v{c}--\v{S}torgel conjecture and a weakening of it by Gartland and Lokshtanov, and by Korhonen.

cs.CC↗

arXiv2026

Topology inside NC$^1$

We show that ACC$^0$ is precisely what can be computed with constant-width circuits of polynomial size and polylogarithmic genus. This extends a characterization given by Hansen, showing that planar constant-width circuits also characterize ACC$^0$. Thus polylogarithmic genus provides no additional computational power in this model. We consider other generalizations of planarity, including crossing number and thickness. We show that constant-width circuits of polynomial size and thickness two already suffice to capture all of NC$^1$.

cs.CC↗