Two-Level Rectilinear Steiner Trees

Given a set $P$ of terminals in the plane and a partition of $P$ into $k$ subsets $P_1, ..., P_k$, a two-level rectilinear Steiner tree consists of a rectilinear Steiner tree $T_i$ connecting the terminals in each set $P_i$ ($i=1,...,k$) and a top-level tree $T_{top}$ connecting the trees $T_1, ..., T_k$. The goal is to minimize the total length of all trees. This problem arises naturally in the design of low-power physical implementations of parity functions on a computer chip. For bounded $k$ we present a polynomial time approximation scheme (PTAS) that is based on Arora's PTAS for rectilinear Steiner trees after lifting each partition into an extra dimension. For the general case we propose an algorithm that predetermines a connection point for each $T_i$ and $T_{top}$ ($i=1,...,k$). Then, we apply any approximation algorithm for minimum rectilinear Steiner trees in the plane to compute each $T_i$ and $T_{top}$ independently. This gives us a $2.37$-factor approximation with a running time of $\mathcal{O}(|P|\log|P|)$ suitable for fast practical computations. The approximation factor reduces to $1.63$ by applying Arora's approximation scheme in the plane

Energy-Efficient Digital Circuit Design using Threshold Logic Gates

abstract: Improving energy efficiency has always been the prime objective of the custom and automated digital circuit design techniques. As a result, a multitude of methods to reduce power without sacrificing performance have been proposed. However, as the field of design automation has matured over the last few decades, there have been no new automated design techniques, that can provide considerable improvements in circuit power, leakage and area. Although emerging nano-devices are expected to replace the existing MOSFET devices, they are far from being as mature as semiconductor devices and their full potential and promises are many years away from being practical. The research described in this dissertation consists of four main parts. First is a new circuit architecture of a differential threshold logic flipflop called PNAND. The PNAND gate is an edge-triggered multi-input sequential cell whose next state function is a threshold function of its inputs. Second a new approach, called hybridization, that replaces flipflops and parts of their logic cones with PNAND cells is described. The resulting \hybrid circuit, which consists of conventional logic cells and PNANDs, is shown to have significantly less power consumption, smaller area, less standby power and less power variation. Third, a new architecture of a field programmable array, called field programmable threshold logic array (FPTLA), in which the standard lookup table (LUT) is replaced by a PNAND is described. The FPTLA is shown to have as much as 50% lower energy-delay product compared to conventional FPGA using well known FPGA modeling tool called VPR. Fourth, a novel clock skewing technique that makes use of the completion detection feature of the differential mode flipflops is described. This clock skewing method improves the area and power of the ASIC circuits by increasing slack on timing paths. An additional advantage of this method is the elimination of hold time violation on given short paths. Several circuit design methodologies such as retiming and asynchronous circuit design can use the proposed threshold logic gate effectively. Therefore, the use of threshold logic flipflops in conventional design methodologies opens new avenues of research towards more energy-efficient circuits.Dissertation/ThesisDoctoral Dissertation Computer Science 201

Approximate logic circuits: Theory and applications

CMOS technology scaling, the process of shrinking transistor dimensions based on Moore's law, has been the thrust behind increasingly powerful integrated circuits for over half a century. As dimensions are scaled to few tens of nanometers, process and environmental variations can significantly alter transistor characteristics, thus degrading reliability and reducing performance gains in CMOS designs with technology scaling. Although design solutions proposed in recent years to improve reliability of CMOS designs are power-efficient, the performance penalty associated with these solutions further reduces performance gains with technology scaling, and hence these solutions are not well-suited for high-performance designs. This thesis proposes approximate logic circuits as a new logic synthesis paradigm for reliable, high-performance computing systems. Given a specification, an approximate logic circuit is functionally equivalent to the given specification for a "significant" portion of the input space, but has a smaller delay and power as compared to a circuit implementation of the original specification. This contributions of this thesis include (i) a general theory of approximation and efficient algorithms for automated synthesis of approximations for unrestricted random logic circuits, (ii) logic design solutions based on approximate circuits to improve reliability of designs with negligible performance penalty, and (iii) efficient decomposition algorithms based on approxiiii mate circuits to improve performance of designs during logic synthesis. This thesis concludes with other potential applications of approximate circuits and identifies. open problems in logic decomposition and approximate circuit synthesis

The 1989 Goddard Conference on Space Applications of Artificial Intelligence

The following topics are addressed: mission operations support; planning and scheduling; fault isolation/diagnosis; image processing and machine vision; data management; and modeling and simulation

Tiled microprocessors

Thesis (Ph. D.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2007.Includes bibliographical references (p. 251-258).Current-day microprocessors have reached the point of diminishing returns due to inherent scalability limitations. This thesis examines the tiled microprocessor, a class of microprocessor which is physically scalable but inherits many of the desirable properties of conventional microprocessors. Tiled microprocessors are composed of an array of replicated tiles connected by a special class of network, the Scalar Operand Network (SON), which is optimized for low-latency, low-occupancy communication between remote ALUs on different tiles. Tiled microprocessors can be constructed to scale to 100's or 1000's of functional units. This thesis identifies seven key criteria for achieving physical scalability in tiled microprocessors. It employs an archetypal tiled microprocessor to examine the challenges in achieving these criteria and to explore the properties of Scalar Operand Networks. The thesis develops the field of SONs in three major ways: it introduces the 5-tuple performance metric, it describes a complete, high-frequency SON implementation, and it proposes a taxonomy, called AsTrO, for categorizing them.(cont.) To develop these ideas, the thesis details the design, implementation and analysis of a tiled microprocessor prototype, the Raw Microprocessor, which was implemented at MIT in 180 nm technology. Overall, compared to Raw, recent commercial processors with half the transistors required 30x as many lines of code, occupied 100x as many designers, contained 50x as many pre-tapeout bugs, and resulted in 33x as many post-tapeout bugs. At the same time, the Raw microprocessor proves to be more versatile in exploiting ILP, stream, and server-farm workloads with modest to large amounts of parallelism.by Michael Bedford Taylor.Ph.D