Synthesis and Verification of Digital Circuits using Functional Simulation and Boolean Satisfiability.

The semiconductor industry has long relied on the steady trend of transistor scaling, that is, the shrinking of the dimensions of silicon transistor devices, as a way to improve the cost and performance of electronic devices. However, several design challenges have emerged as transistors have become smaller. For instance, wires are not scaling as fast as transistors, and delay associated with wires is becoming more significant. Moreover, in the design flow for integrated circuits, accurate modeling of wire-related delay is available only toward the end of the design process, when the physical placement of logic units is known. Consequently, one can only know whether timing performance objectives are satisfied, i.e., if timing closure is achieved, after several design optimizations. Unless timing closure is achieved, time-consuming design-flow iterations are required. Given the challenges arising from increasingly complex designs, failing to quickly achieve timing closure threatens the ability of designers to produce high-performance chips that can match continually growing consumer demands. In this dissertation, we introduce powerful constraint-guided synthesis optimizations that take into account upcoming timing closure challenges and eliminate expensive design iterations. In particular, we use logic simulation to approximate the behavior of increasingly complex designs leveraging a recently proposed concept, called bit signatures, which allows us to represent a large fraction of a complex circuit's behavior in a compact data structure. By manipulating these signatures, we can efficiently discover a greater set of valid logic transformations than was previously possible and, as a result, enhance timing optimization. Based on the abstractions enabled through signatures, we propose a comprehensive suite of novel techniques: (1) a fast computation of circuit don't-cares that increases restructuring opportunities, (2) a verification methodology to prove the correctness of speculative optimizations that efficiently utilizes the computational power of modern multi-core systems, and (3) a physical synthesis strategy using signatures that re-implements sections of a critical path while minimizing perturbations to the existing placement. Our results indicate that logic simulation is effective in approximating the behavior of complex designs and enables a broader family of optimizations than previous synthesis approaches.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/61793/1/splaza_1.pd

Broadening the Scope of Multi-Objective Optimizations in Physical Synthesis of Integrated Circuits.

In modern VLSI design, physical synthesis tools are primarily responsible for satisfying chip-performance constraints by invoking a broad range of circuit optimizations, such as buffer insertion, logic restructuring, gate sizing and relocation. This process is known as timing closure. Our research seeks more powerful and efficient optimizations to improve the state of the art in modern chip design. In particular, we integrate timing-driven relocation, retiming, logic cloning, buffer insertion and gate sizing in novel ways to create powerful circuit transformations that help satisfy setup-time constraints. State-of-the-art physical synthesis optimizations are typically applied at two scales: i) global algorithms that affect the entire netlist and ii) local transformations that focus on a handful of gates or interconnections. The scale of modern chip designs dictates that only near-linear-time optimization algorithms can be applied at the global scope — typically limited to wirelength-driven placement and legalization. Localized transformations can rely on more time-consuming optimizations with accurate delay models. Few techniques bridge the gap between fully-global and localized optimizations. This dissertation broadens the scope of physical synthesis optimization to include accurate transformations operating between the global and local scales. In particular, we integrate groups of related transformations to break circular dependencies and increase the number of circuit elements that can be jointly optimized to escape local minima. Integrated transformations in this dissertation are developed by identifying and removing obstacles to successful optimizations. Integration is achieved through mapping multiple operations to rigorous mathematical optimization problems that can be solved simultaneously. We achieve computational scalability in our techniques by leveraging analytical delay models and focusing optimization efforts on carefully selected regions of the chip. In this regard, we make extensive use of a linear interconnect-delay model that accounts for the impact of subsequent repeated insertion. Our integrated transformations are evaluated on high-performance circuits with over 100,000 gates. Integrated optimization techniques described in this dissertation ensure graceful timing-closure process and impact nearly every aspect of a typical physical synthesis flow. They have been validated in EDA tools used at IBM for physical synthesis of high-performance CPU and ASIC designs, where they significantly improved chip performance.Ph.D.Computer Science & EngineeringUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/78744/1/iamyou_1.pd

Circuit delay optimization by buffering the logic gates

Avec la miniaturisation actuelle, les circuits démontrent de plus en plus l'importance des délais d'interconnexion. Afin de réduire ce délai, l'insertion de tampons doit être effectuée durant la synthèse logique et la synthèse physique. Cette activité d'optimisation est souvent basée sur la programmation dynamique. Dans ce mémoire, la technique branch-and-bound est utilisé et le problème pour le cas spécifique d'arbres de tampons équilibrés est résolu, où toutes les charges ont un temps requis et une capacité identique. Une analyse mathématique est faite pour tenir compte d'une variété de questions de conception telles que la topologie, la bibliothèque de tampons et le changement de phase en présence d'inverseur. En combinant la programmation dynamique et les techniques branch-and-bound, une méthode hybride est présentée qui améliore le temps d'exécution tout en conservant une utilisation de mémoire raisonnable. Les concepts mathématiques et algorithmiques fondamentaux utilisés dans ce mémoire peuvent être employés pour généraliser la méthode proposée pour un ensemble de charges avec des capacités et des temps requis différents

Overcoming the challenges in very deep submicron for area reduction, power reduction and faster design closure

The project is aimed at understanding the existing very deep sub-micron (VDSM) implementation of a digital design, analyzing it from the point of view of power, area and timing and to come up with solutions and strategies to optimize the implementation in terms of power, area and timing. The effort involved, to understand the constraints, reasons and the requirements resulting in the existing implementation of the design. Further, various experiments were carried out to improve the design in various aspects like power, area and timing. The tradeoffs required and the benefits of each of the experiments were contrasted and analyzed. The optimum solutions and strategies which balance the requirements were tried out and published at the end of the report

Algorithms for Circuit Sizing in VLSI Design

One of the key problems in the physical design of computer chips, also known as integrated circuits, consists of choosing a  physical layout  for the logic gates and memory circuits (registers) on the chip. The layouts have a high influence on the power consumption and area of the chip and the delay of signal paths.  A discrete set of predefined layouts  for each logic function and register type with different physical properties is given by a library. One of the most influential characteristics of a circuit defined by the layout is its size. In this thesis we present new algorithms for the problem of choosing sizes for the circuits and its continuous relaxation,  and  evaluate these in theory and practice. A popular approach is based on Lagrangian relaxation and projected subgradient methods. We show that seemingly heuristic modifications that have been proposed for this approach can be theoretically justified by applying the well-known multiplicative weights algorithm. Subsequently, we propose a new model for the sizing problem as a min-max resource sharing problem. In our context, power consumption and signal delays are represented by resources that are distributed to customers. Under certain assumptions we obtain a polynomial time approximation for the continuous relaxation of the sizing problem that improves over the Lagrangian relaxation based approach. The new resource sharing algorithm has been implemented as part of the BonnTools software package which is developed at the Research Institute for Discrete Mathematics at the University of Bonn in cooperation with IBM. Our experiments on the ISPD 2013 benchmarks and state-of-the-art microprocessor designs provided by IBM illustrate that the new algorithm exhibits more stable convergence behavior compared to a Lagrangian relaxation based algorithm. Additionally, better timing and reduced power consumption was achieved on almost all instances. A subproblem of the new algorithm consists of finding sizes minimizing a weighted sum of power consumption and signal delays. We describe a method that approximates the continuous relaxation of this problem in polynomial time under certain assumptions. For the discrete problem we provide a fully polynomial approximation scheme under certain assumptions on the topology of the chip. Finally, we present a new algorithm for timing-driven optimization of registers. Their sizes and locations on a chip are usually determined during the clock network design phase, and remain mostly unchanged afterwards although the timing criticalities on which they were based can change. Our algorithm permutes register positions and sizes within so-called  clusters  without impairing the clock network such that it can be applied late in a design flow. Under mild assumptions, our algorithm finds an optimal solution which maximizes the worst cluster slack. It is implemented as part of the BonnTools and improves timing of registers on state-of-the-art microprocessor designs by up to 7.8% of design cycle time. </div

Efficient alternative wiring techniques and applications.

Sze, Chin Ngai.Thesis (M.Phil.)--Chinese University of Hong Kong, 2001.Includes bibliographical references (leaves 80-84) and index.Abstracts in English and Chinese.Abstract --- p.iAcknowledgments --- p.iiiCurriculum Vitae --- p.ivList of Figures --- p.ixList of Tables --- p.xiiChapter 1 --- Introduction --- p.1Chapter 1.1 --- Motivation and Aims --- p.1Chapter 1.2 --- Contribution --- p.8Chapter 1.3 --- Organization of Dissertation --- p.10Chapter 2 --- Definitions and Notations --- p.11Chapter 3 --- Literature Review --- p.15Chapter 3.1 --- Logic Reconstruction --- p.15Chapter 3.1.1 --- SIS: A System for Sequential and Combinational Logic Synthesis --- p.16Chapter 3.2 --- ATPG-based Alternative Wiring --- p.17Chapter 3.2.1 --- Redundancy Addition and Removal for Logic Optimization --- p.18Chapter 3.2.2 --- Perturb and Simplify Logic Optimization --- p.18Chapter 3.2.3 --- REWIRE --- p.21Chapter 3.2.4 --- Implication-tree Based Alternative Wiring Logic Trans- formation --- p.22Chapter 3.3 --- Graph-based Alternative Wiring --- p.24Chapter 4 --- Implication Based Alternative Wiring Logic Transformation --- p.25Chapter 4.1 --- Source Node Implication --- p.25Chapter 4.1.1 --- Introduction --- p.25Chapter 4.1.2 --- Implication Relationship and Implication-tree --- p.25Chapter 4.1.3 --- Selection of Alternative Wire Based on Implication-tree --- p.29Chapter 4.1.4 --- Implication-tree Based Logic Transformation --- p.32Chapter 4.2 --- Destination Node Implication --- p.35Chapter 4.2.1 --- Introduction --- p.35Chapter 4.2.2 --- Destination Node Relationship --- p.35Chapter 4.2.3 --- Destination Node Implication-tree --- p.39Chapter 4.2.4 --- Selection of Alternative Wire --- p.41Chapter 4.3 --- The Algorithm --- p.43Chapter 4.3.1 --- IB AW Implementation --- p.43Chapter 4.3.2 --- Experimental Results --- p.43Chapter 4.4 --- Conclusion --- p.45Chapter 5 --- Graph Based Alternative Wiring Logic Transformation --- p.47Chapter 5.1 --- Introduction --- p.47Chapter 5.2 --- Notations and Definitions --- p.48Chapter 5.3 --- Alternative Wire Patterns --- p.50Chapter 5.4 --- Construction of Minimal Patterns --- p.54Chapter 5.4.1 --- Minimality of Patterns --- p.54Chapter 5.4.2 --- Minimal Pattern Formation --- p.56Chapter 5.4.3 --- Pattern Extraction --- p.61Chapter 5.5 --- Experimental Results --- p.63Chapter 5.6 --- Conclusion --- p.63Chapter 6 --- Logic Optimization by GBAW --- p.66Chapter 6.1 --- Introduction --- p.66Chapter 6.2 --- Logic Simplification --- p.67Chapter 6.2.1 --- Single-Addition-Multiple-Removal by Pattern Feature . . --- p.67Chapter 6.2.2 --- Single-Addition-Multiple-Removal by Combination of Pat- terns --- p.68Chapter 6.2.3 --- Single-Addition-Single-Removal --- p.70Chapter 6.3 --- Incremental Perturbation Heuristic --- p.71Chapter 6.4 --- GBAW Optimization Algorithm --- p.73Chapter 6.5 --- Experimental Results --- p.73Chapter 6.6 --- Conclusion --- p.76Chapter 7 --- Conclusion --- p.78Bibliography --- p.80Chapter A --- VLSI Design Cycle --- p.85Chapter B --- Alternative Wire Patterns in [WLFOO] --- p.87Chapter B.1 --- 0-local Pattern --- p.87Chapter B.2 --- 1-local Pattern --- p.88Chapter B.3 --- 2-local Pattern --- p.89Chapter B.4 --- Fanout-reconvergent Pattern --- p.90Chapter C --- New Alternative Wire Patterns --- p.91Chapter C.1 --- Pattern Cluster C1 --- p.91Chapter C.1.1 --- NAND-NAND-AND/NAND;AND/NAND --- p.91Chapter C.1.2 --- NOR-NOR-OR/NOR;AND/NAND --- p.92Chapter C.1.3 --- AND-NOR-OR/NOR;OR/NOR --- p.95Chapter C.1.4 --- OR-NAND-AND/NAND;AND/NAND --- p.95Chapter C.2 --- Pattern Cluster C2 --- p.98Chapter C.3 --- Pattern Cluster C3 --- p.99Chapter C.4 --- Pattern Cluster C4 --- p.104Chapter C.5 --- Pattern Cluster C5 --- p.105Glossary --- p.106Index --- p.10

Area-power-delay trade-off in logic synthesis

This thesis introduces new concepts to perform area-power-delay trade-offs in a logic synthesis system. To achieve this, a new delay model is presented, which gives accurate delay estimations for arbitrary sets of Boolean expressions. This allows use of this delay model already during the very first steps of logic synthesis. Furthermore, new algorithms are presented for a number of different optimization tasks within logic synthesis. There are new algorithms to create prime irredundant Boo lean expressions, to perform technology mapping for use with standard cell generators, and to perform gate sizing. To prove the validity of the presented ideas, benchmark results are given throughout the thesis

Synthesis and Optimization of Reversible Circuits - A Survey

Reversible logic circuits have been historically motivated by theoretical research in low-power electronics as well as practical improvement of bit-manipulation transforms in cryptography and computer graphics. Recently, reversible circuits have attracted interest as components of quantum algorithms, as well as in photonic and nano-computing technologies where some switching devices offer no signal gain. Research in generating reversible logic distinguishes between circuit synthesis, post-synthesis optimization, and technology mapping. In this survey, we review algorithmic paradigms --- search-based, cycle-based, transformation-based, and BDD-based --- as well as specific algorithms for reversible synthesis, both exact and heuristic. We conclude the survey by outlining key open challenges in synthesis of reversible and quantum logic, as well as most common misconceptions.Comment: 34 pages, 15 figures, 2 table