Two Level Boolean Minimization Using a Small Digital Computer

Electrical Engineerin

BOOM - A Heuristic Boolean Minimizer

This paper presents an algorithm for two-level Boolean minimization (BOOM) based on a new implicant generation paradigm. In contrast to all previous minimization methods, where the implicants are generated bottom-up, the proposed method uses a top-down approach. Thus, instead of increasing the dimensionality of implicants by omitting literals from their terms, the dimension of a term is gradually decreased by adding new literals. The method is advantageous especially for functions with many input variables (up to thousands) and with only few care terms defined, where other minimization tools are not applicable because of the long runtime. The method has been tested on several different kinds of problems and the results were compared with ESPRESSO

MILO : a microarchitecture and logic optimizer

In this report we discuss strengths and weaknesses of logic synthesis systems and describe a system for microarchitectural and logic optimization. Our system uses a set of algorithms for synthesizing SSI/MSI macros from parameterized microarchitecture components. In addition, it uses rules for optimizing both at the microarchitecture and logic level. The system increases designer productivity and requires less design knowledge and experience from circuit engineers

Custom Integrated Circuits

Contains reports on twelve research projects.Analog Devices, Inc.International Business Machines, Inc.Joint Services Electronics Program (Contract DAAL03-86-K-0002)Joint Services Electronics Program (Contract DAAL03-89-C-0001)U.S. Air Force - Office of Scientific Research (Grant AFOSR 86-0164)Rockwell International CorporationOKI Semiconductor, Inc.U.S. Navy - Office of Naval Research (Contract N00014-81-K-0742)Charles Stark Draper LaboratoryNational Science Foundation (Grant MIP 84-07285)National Science Foundation (Grant MIP 87-14969)Battelle LaboratoriesNational Science Foundation (Grant MIP 88-14612)DuPont CorporationDefense Advanced Research Projects Agency/U.S. Navy - Office of Naval Research (Contract N00014-87-K-0825)American Telephone and TelegraphDigital Equipment CorporationNational Science Foundation (Grant MIP-88-58764

A system for microarchitecture and logic optimization

This thesis spans two levels of the design process by examining optimization at both the register-transfer level and at the logic level. More specifically, this thesis addresses the following two problems: 1) performing logic synthesis for custom layout rather than the traditional approach that focuses on synthesis for standard cells, and 2) performing optimization for custom layout from register-transfer level netlists. Thus optimization is performed on the microarchitecture design and at a lower level for individual microarchitecture components.First, techniques are introduced for generating gate-level netlists that take advantage of custom layout capabilities. Such techniques include limiting serial/parallel transistor chains, transistor sizes, and capacitive loads in forming complex gates. These considerations have not been incorporated in previous logic synthesis systems.Second, techniques are introduced for improving the microarchitecture structure and using estimates from lower-level optimization tools to guide microarchitecture design optimizations that attempt to meet user specified area and time constraints. These techniques include the capability for mixing layout styles such as custom layout for random-logic components and bit-slicing for regularly structured components. In this manner the entire design, control logic and datapath, can be optimized at the same time. Further, this paper presents a new methodology for microarchitecture-level optimization that greatly reduces the amount of technology-specific knowledge necessary to perform the optimizations

Improved handling of the decoding operation in the Presto compiler

Thesis (M. Eng. and S.B.)--Massachusetts Institute of Technology, Dept. of Electrical Engineering and Computer Science, 2004.Includes bibliographical references (leaves 62-63).This thesis presents a research project on decoder related optimizations in HDL de- signs. The goal of the research is to improve design synthesis quality-of-result, mainly in terms of area; this involves sharing decoders driven by related inputs, and map decoders using fewer number of boolean gates. Algorithms presented in this thesis were implemented in the Presto HDL compiler. A series of tests were conducted using real-world HDL designs in order to determine how effective these optimizations are.by Wenyan Dong.M.Eng.and S.B

Modeling and synthesis of approximate digital circuits

textEnergy minimization has become an ever more important concern in the design of very large scale integrated circuits (VLSI). In recent years, approximate computing, which is based on the idea of trading off computational accuracy for improved energy efficiency, has attracted significant attention. Applications that are both compute-intensive and error-tolerant are most suitable to adopt approximation strategies. This includes digital signal processing, data mining, machine learning or search algorithms. Such approximations can be achieved at several design levels, ranging from software, algorithm and architecture, down to logic or transistor levels. This dissertation investigates two research threads for the derivation of approximate digital circuits at the logic level: 1) modeling and synthesis of fundamental arithmetic building blocks; 2) automated techniques for synthesizing arbitrary approximate logic circuits under general error specifications. The first thread investigates elementary arithmetic blocks, such as adders and multipliers, which are at the core of all data processing and often consume most of the energy in a circuit. An optimal strategy is developed to reduce energy consumption in timing-starved adders under voltage over-scaling. This allows a formal demonstration that, under quadratic error measures prevalent in signal processing applications, an adder design strategy that separates the most significant bits (MSBs) from the least significant bits (LSBs) is optimal. An optimal conditional bounding (CB) logic is further proposed for the LSBs, which selectively compensates for the occurrence of errors in the MSB part. There is a rich design space of optimal adders defined by different CB solutions. The other thread considers the problem of approximate logic synthesis (ALS) in two-level form. ALS is concerned with formally synthesizing a minimum-cost approximate Boolean function, whose behavior deviates from a specified exact Boolean function in a well-constrained manner. It is established that the ALS problem un-constrained by the frequency of errors is isomorphic to a Boolean relation (BR) minimization problem, and hence can be efficiently solved by existing BR minimizers. An efficient heuristic is further developed which iteratively refines the magnitude-constrained solution to arrive at a two-level representation also satisfying error frequency constraints. To extend the two-level solution into an approach for multi-level approximate logic synthesis (MALS), Boolean network simplifications allowed by external don't cares (EXDCs) are used. The key contribution is in finding non-trivial EXDCs that can maximally approach the external BR and, when applied to the Boolean network, solve the MALS problem constrained by magnitude only. The algorithm then ensures compliance to error frequency constraints by recovering the correct outputs on the sought number of error-producing inputs while aiming to minimize the network cost increase. Experiments have demonstrated the effectiveness of the proposed techniques in deriving approximate circuits. The approximate adders can save up to 60% energy compared to exact adders for a reasonable accuracy. When used in larger systems implementing image-processing algorithms, energy savings of 40% are possible. The logic synthesis approaches generally can produce approximate Boolean functions or networks with complexity reductions ranging from 30% to 50% under small error constraints.Electrical and Computer Engineerin