Search arXivSearch

arXiv · 0705.4320

Defect-Tolerant CMOL Cell Assignment via Satisfiability

Abstract

We present a CAD framework for CMOL, a hybrid CMOS/ molecular circuit architecture. Our framework first transforms any logically synthesized circuit based on AND/OR/NOT gates to a NOR gate circuit, and then maps the NOR gates to CMOL. We encode the CMOL cell assignment problem as boolean conditions. The boolean constraint is satisfiable if and only if there is a way to map all the NOR gates to the CMOL cells. We further investigate various types of static defects for the CMOL architecture, and propose a reconfiguration technique that can deal with these defects through our CAD framework. This is the first automated framework for CMOL cell assignment, and the first to model several different CMOL static defects. Empirical results show that our approach is efficient and scalable.

Explore related subjects

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

William N. N. Hung, Changjian Gao, Xiaoyu Song, Dan Hammerstrom. 2007-05-29. Defect-Tolerant CMOL Cell Assignment via Satisfiability. https://arxiv.org/abs/0705.4320

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

KEEP EXPLORING

Related papers

Pimp my fixpoint: sofic realization of multidimensional substitution-based shift spaces

In symbolic dynamics, the fixed-point construction from arXiv:0910.2415 defines shift spaces of finite type whose configurations embed infinite hierarchies of tilings. This article provides a "black box" abstraction of this method phrased in terms of substitutions and $S$-adic limit spaces operating over sequences of increasingly large alphabets. By quantifying the amount of information computed by the substitutions at each level, and using a suitable parallel model of computation, we provide a simple positive criterion of multidimensional soficity that generalizes classical examples from the literature.

cs.DM

Flip Dynamics for Sampling Colorings: Improving $(11/6-ε)$ Using a Simple Metric

We present improved bounds for randomly sampling $k$-colorings of graphs with maximum degree $Δ$; our results hold without any further structural assumptions on the graph. The Glauber dynamics is a simple single-site update Markov chain. Jerrum (1995) proved an optimal $O(n\log{n})$ mixing-time bound for Glauber dynamics whenever $k>2Δ$ where $Δ$ is the maximum degree of the input graph. This bound was improved by Vigoda (1999) to $k>(11/6)Δ$ using a "flip" dynamics which recolors (small) maximal two-colored components in each step. Vigoda's result was the best known for general graphs for 20 years until Chen et al. (2019) established optimal mixing of the flip dynamics for $k>(11/6-\varepsilon)Δ$ where $\varepsilon\approx 10^{-5}$. We present the first substantial improvement over these results. We prove an optimal mixing-time bound of $O(n\log{n})$ for the flip dynamics when $Δ\geq125$ and $k\geq1.809Δ$. This yields, through recent spectral independence results, an optimal $O(n\log{n})$ mixing time for the Glauber dynamics for every fixed $Δ\geq125$ in the same range of $k/Δ$. Our proof utilizes path coupling with a simple weighted Hamming distance for "unblocked" neighbors.

cs.DM