Relaxation Techniques for the Simulation of VLSI Circuits

Download Relaxation Techniques for the Simulation of VLSI Circuits PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461322715
Total Pages : 202 pages
Book Rating : 4.4/5 (613 download)

DOWNLOAD NOW!


Book Synopsis Relaxation Techniques for the Simulation of VLSI Circuits by : Jacob K. White

Download or read book Relaxation Techniques for the Simulation of VLSI Circuits written by Jacob K. White and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Circuit simulation has been a topic of great interest to the integrated circuit design community for many years. It is a difficult, and interesting, problem be cause circuit simulators are very heavily used, consuming thousands of computer hours every year, and therefore the algorithms must be very efficient. In addi tion, circuit simulators are heavily relied upon, with millions of dollars being gambled on their accuracy, and therefore the algorithms must be very robust. At the University of California, Berkeley, a great deal of research has been devoted to the study of both the numerical properties and the efficient imple mentation of circuit simulation algorithms. Research efforts have led to several programs, starting with CANCER in the 1960's and the enormously successful SPICE program in the early 1970's, to MOTIS-C, SPLICE, and RELAX in the late 1970's, and finally to SPLICE2 and RELAX2 in the 1980's. Our primary goal in writing this book was to present some of the results of our current research on the application of relaxation algorithms to circuit simu lation. As we began, we realized that a large body of mathematical and exper imental results had been amassed over the past twenty years by graduate students, professors, and industry researchers working on circuit simulation. It became a secondary goal to try to find an organization of this mass of material that was mathematically rigorous, had practical relevance, and still retained the natural intuitive simplicity of the circuit simulation subject.

Relaxation Techniques for the Simulation of VLSI Circuits

Download Relaxation Techniques for the Simulation of VLSI Circuits PDF Online Free

Author :
Publisher : Springer
ISBN 13 : 9781461322726
Total Pages : 202 pages
Book Rating : 4.3/5 (227 download)

DOWNLOAD NOW!


Book Synopsis Relaxation Techniques for the Simulation of VLSI Circuits by : Jacob K. White

Download or read book Relaxation Techniques for the Simulation of VLSI Circuits written by Jacob K. White and published by Springer. This book was released on 2011-10-12 with total page 202 pages. Available in PDF, EPUB and Kindle. Book excerpt: Circuit simulation has been a topic of great interest to the integrated circuit design community for many years. It is a difficult, and interesting, problem be cause circuit simulators are very heavily used, consuming thousands of computer hours every year, and therefore the algorithms must be very efficient. In addi tion, circuit simulators are heavily relied upon, with millions of dollars being gambled on their accuracy, and therefore the algorithms must be very robust. At the University of California, Berkeley, a great deal of research has been devoted to the study of both the numerical properties and the efficient imple mentation of circuit simulation algorithms. Research efforts have led to several programs, starting with CANCER in the 1960's and the enormously successful SPICE program in the early 1970's, to MOTIS-C, SPLICE, and RELAX in the late 1970's, and finally to SPLICE2 and RELAX2 in the 1980's. Our primary goal in writing this book was to present some of the results of our current research on the application of relaxation algorithms to circuit simu lation. As we began, we realized that a large body of mathematical and exper imental results had been amassed over the past twenty years by graduate students, professors, and industry researchers working on circuit simulation. It became a secondary goal to try to find an organization of this mass of material that was mathematically rigorous, had practical relevance, and still retained the natural intuitive simplicity of the circuit simulation subject.

Circuit Simulation Methods and Algorithms

Download Circuit Simulation Methods and Algorithms PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 1351460633
Total Pages : 490 pages
Book Rating : 4.3/5 (514 download)

DOWNLOAD NOW!


Book Synopsis Circuit Simulation Methods and Algorithms by : Jan Ogrodzki

Download or read book Circuit Simulation Methods and Algorithms written by Jan Ogrodzki and published by CRC Press. This book was released on 2018-05-04 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt: Circuit Simulation Methods and Algorithms provides a step-by-step theoretical consideration of methods, techniques, and algorithms in an easy-to-understand format. Many illustrations explain more difficult problems and present instructive circuits. The book works on three levels: The simulator-user level for practitioners and students who want to better understand circuit simulators. The basic theoretical level, with examples, dedicated to students and beginning researchers. The thorough level for deep insight into circuit simulation based on computer experiments using PSPICE and OPTIMA. Only basic mathematical knowledge, such as matrix algebra, derivatives, and integrals, is presumed.

Algorithms & Architectures For Parallel Processing, 4th Intl Conf

Download Algorithms & Architectures For Parallel Processing, 4th Intl Conf PDF Online Free

Author :
Publisher : World Scientific
ISBN 13 : 9814492019
Total Pages : 745 pages
Book Rating : 4.8/5 (144 download)

DOWNLOAD NOW!


Book Synopsis Algorithms & Architectures For Parallel Processing, 4th Intl Conf by : Andrzej Marian Goscinski

Download or read book Algorithms & Architectures For Parallel Processing, 4th Intl Conf written by Andrzej Marian Goscinski and published by World Scientific. This book was released on 2000-11-24 with total page 745 pages. Available in PDF, EPUB and Kindle. Book excerpt: ICA3PP 2000 was an important conference that brought together researchers and practitioners from academia, industry and governments to advance the knowledge of parallel and distributed computing. The proceedings constitute a well-defined set of innovative research papers in two broad areas of parallel and distributed computing: (1) architectures, algorithms and networks; (2) systems and applications.

Computational Methods In Large Scale Simulation

Download Computational Methods In Large Scale Simulation PDF Online Free

Author :
Publisher : World Scientific
ISBN 13 : 9814480207
Total Pages : 395 pages
Book Rating : 4.8/5 (144 download)

DOWNLOAD NOW!


Book Synopsis Computational Methods In Large Scale Simulation by : Heow-pueh Lee

Download or read book Computational Methods In Large Scale Simulation written by Heow-pueh Lee and published by World Scientific. This book was released on 2005-10-26 with total page 395 pages. Available in PDF, EPUB and Kindle. Book excerpt: This volume documents the research carried out by visiting scientists attached to the Institute for Mathematical Sciences (IMS) at the National University of Singapore and the Institute of High Performance Computing (IHPC) under the program “Advances and Mathematical Issues in Large Scale Simulation.” From 2002 to 2003, researchers from various countries gathered to initiate interesting and innovative work on various themes related to multiscale simulation and fast algorithms.Today, modeling and simulation are used extensively to solve complex problems and to reduce the use of experimentation during the design and analysis stage. It is important to know the various issues that have to be considered in the successful development of computational methodologies for such work.This volume is a compilation of the research by various visiting scientists in the area of modeling and multiscale simulation. Each article covers a major project and documents how computational methodology, mathematical modeling, high performance computing and simulation are combined in a multiscale scheme to solve a variety of complex problems. Some of these include the design, synthesis, processing, characterization and manufacture of nanomaterials and nanostructures, new algorithms for computational work, and grid computing.Through the included examples, readers can realize the vast potential of computational modeling and large scale simulation for the solution of problems in a variety of disciplines and applications.

Switch-Level Timing Simulation of MOS VLSI Circuits

Download Switch-Level Timing Simulation of MOS VLSI Circuits PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461317096
Total Pages : 218 pages
Book Rating : 4.4/5 (613 download)

DOWNLOAD NOW!


Book Synopsis Switch-Level Timing Simulation of MOS VLSI Circuits by : Vasant B. Rao

Download or read book Switch-Level Timing Simulation of MOS VLSI Circuits written by Vasant B. Rao and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 218 pages. Available in PDF, EPUB and Kindle. Book excerpt: Only two decades ago most electronic circuits were designed with a slide-rule, and the designs were verified using breadboard techniques. Simulation tools were a research curiosity and in general were mistrusted by most designers and test engineers. In those days the programs were not user friendly, models were inadequate, and the algorithms were not very robust. The demand for simulation tools has been driven by the increasing complexity of integrated circuits and systems, and it has been aided by the rapid decrease in the cost of com puting that has occurred over the past several decades. Today a wide range of tools exist for analYSiS, deSign, and verification, and expert systems and synthesis tools are rapidly emerging. In this book only one aspect of the analysis and design process is examined. but it is a very important aspect that has received much attention over the years. It is the problem of accurate circuit and timing simulation.

Simulated Annealing for VLSI Design

Download Simulated Annealing for VLSI Design PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461316774
Total Pages : 206 pages
Book Rating : 4.4/5 (613 download)

DOWNLOAD NOW!


Book Synopsis Simulated Annealing for VLSI Design by : D.F. Wong

Download or read book Simulated Annealing for VLSI Design written by D.F. Wong and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 206 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph represents a summary of our work in the last two years in applying the method of simulated annealing to the solution of problems that arise in the physical design of VLSI circuits. Our study is experimental in nature, in that we are con cerned with issues such as solution representations, neighborhood structures, cost functions, approximation schemes, and so on, in order to obtain good design results in a reasonable amount of com putation time. We hope that our experiences with the techniques we employed, some of which indeed bear certain similarities for different problems, could be useful as hints and guides for other researchers in applying the method to the solution of other prob lems. Work reported in this monograph was partially supported by the National Science Foundation under grant MIP 87-03273, by the Semiconductor Research Corporation under contract 87-DP- 109, by a grant from the General Electric Company, and by a grant from the Sandia Laboratories.

Automatic Speech Recognition

Download Automatic Speech Recognition PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461536502
Total Pages : 216 pages
Book Rating : 4.4/5 (615 download)

DOWNLOAD NOW!


Book Synopsis Automatic Speech Recognition by : Kai-Fu Lee

Download or read book Automatic Speech Recognition written by Kai-Fu Lee and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: Speech Recognition has a long history of being one of the difficult problems in Artificial Intelligence and Computer Science. As one goes from problem solving tasks such as puzzles and chess to perceptual tasks such as speech and vision, the problem characteristics change dramatically: knowledge poor to knowledge rich; low data rates to high data rates; slow response time (minutes to hours) to instantaneous response time. These characteristics taken together increase the computational complexity of the problem by several orders of magnitude. Further, speech provides a challenging task domain which embodies many of the requirements of intelligent behavior: operate in real time; exploit vast amounts of knowledge, tolerate errorful, unexpected unknown input; use symbols and abstractions; communicate in natural language and learn from the environment. Voice input to computers offers a number of advantages. It provides a natural, fast, hands free, eyes free, location free input medium. However, there are many as yet unsolved problems that prevent routine use of speech as an input device by non-experts. These include cost, real time response, speaker independence, robustness to variations such as noise, microphone, speech rate and loudness, and the ability to handle non-grammatical speech. Satisfactory solutions to each of these problems can be expected within the next decade. Recognition of unrestricted spontaneous continuous speech appears unsolvable at present. However, by the addition of simple constraints, such as clarification dialog to resolve ambiguity, we believe it will be possible to develop systems capable of accepting very large vocabulary continuous speechdictation.

Adaptive Filters and Equalisers

Download Adaptive Filters and Equalisers PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461317010
Total Pages : 200 pages
Book Rating : 4.4/5 (613 download)

DOWNLOAD NOW!


Book Synopsis Adaptive Filters and Equalisers by : Bernard Mulgrew

Download or read book Adaptive Filters and Equalisers written by Bernard Mulgrew and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: The work presented in this text relates to research work in the general area of adaptive filter theory and practice which has been carried out at the Department of Electrical Engineering, University of Edinburgh since 1977. Much of the earlier work in the department was devoted to looking at the problems associated with the physical implementation of these structures. This text relates to research which has been undertaken since 1984 which is more involved with the theoretical development of adaptive algorithms. The text sets out to provide a coherent framework within which general adaptive algorithms for finite impulse response adaptive filters may be evaluated. It further presents one approach to the problem of finding a stable solution to the infinite impulse response adaptive filter problem. This latter objective being restricted to the communications equaliser application area. The authors are indebted to a great number of people for their help, guidance and encouragement during the course of preparing this text. We should first express our appreciation for the support given by two successive heads of department at Edinburgh, Professor J. H. Collins and Professor J. Mavor. The work reported here could not have taken place without their support and also that of many colleagues, principally Professor P. M. Grant who must share much of the responsibility for instigating this line of research at Edinburgh.

Computer-Aided Design of Analog Integrated Circuits and Systems

Download Computer-Aided Design of Analog Integrated Circuits and Systems PDF Online Free

Author :
Publisher : John Wiley & Sons
ISBN 13 : 047122782X
Total Pages : 773 pages
Book Rating : 4.4/5 (712 download)

DOWNLOAD NOW!


Book Synopsis Computer-Aided Design of Analog Integrated Circuits and Systems by : Rob A. Rutenbar

Download or read book Computer-Aided Design of Analog Integrated Circuits and Systems written by Rob A. Rutenbar and published by John Wiley & Sons. This book was released on 2002-05-06 with total page 773 pages. Available in PDF, EPUB and Kindle. Book excerpt: The tools and techniques you need to break the analog design bottleneck! Ten years ago, analog seemed to be a dead-end technology. Today, System-on-Chip (SoC) designs are increasingly mixed-signal designs. With the advent of application-specific integrated circuits (ASIC) technologies that can integrate both analog and digital functions on a single chip, analog has become more crucial than ever to the design process. Today, designers are moving beyond hand-crafted, one-transistor-at-a-time methods. They are using new circuit and physical synthesis tools to design practical analog circuits; new modeling and analysis tools to allow rapid exploration of system level alternatives; and new simulation tools to provide accurate answers for analog circuit behaviors and interactions that were considered impossible to handle only a few years ago. To give circuit designers and CAD professionals a better understanding of the history and the current state of the art in the field, this volume collects in one place the essential set of analog CAD papers that form the foundation of today's new analog design automation tools. Areas covered are: * Analog synthesis * Symbolic analysis * Analog layout * Analog modeling and analysis * Specialized analog simulation * Circuit centering and yield optimization * Circuit testing Computer-Aided Design of Analog Integrated Circuits and Systems is the cutting-edge reference that will be an invaluable resource for every semiconductor circuit designer and CAD professional who hopes to break the analog design bottleneck.

The Bounding Approach to VLSI Circuit Simulation

Download The Bounding Approach to VLSI Circuit Simulation PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1468498916
Total Pages : 231 pages
Book Rating : 4.4/5 (684 download)

DOWNLOAD NOW!


Book Synopsis The Bounding Approach to VLSI Circuit Simulation by : C.A. Zukowski

Download or read book The Bounding Approach to VLSI Circuit Simulation written by C.A. Zukowski and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 231 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book proposes a new approach to circuit simulation that is still in its infancy. The reason for publishing this work as a monograph at this time is to quickly distribute these ideas to the research community for further study. The book is based on a doctoral dissertation undertaken at MIT between 1982 and 1985. In 1982 the author joined a research group that was applying bounding techniques to simple VLSI timing analysis models. The conviction that bounding analysis could also be successfully applied to sophisticated digital MOS circuit models led to the research presented here. Acknowledgments 'me author would like to acknowledge many helpful discussions and much support from his research group at MIT, including Lance Glasser, John Wyatt, Jr. , and Paul Penfield, Jr. Many others have also contributed to this work in some way, including Albert Ruchli, Mark Horowitz, Rich Zippel, Chtis Terman, Jacob White, Mark Matson, Bob Armstrong, Steve McCormick, Cyrus Bamji, John Wroclawski, Omar Wing, Gary Dare, Paul Bassett, and Rick LaMaire. The author would like to give special thanks to his wife, Deborra, for her support and many contributions to the presentation of this research. The author would also like to thank his parents for their encouragement, and IBM for its financial support of t,I-Jis project through a graduate fellowship. THE BOUNDING APPROACH TO VLSI CIRCUIT SIMULATION 1. INTRODUCTION The VLSI revolution of the 1970's has created a need for new circuit analysis techniques.

Microwave Integrated Circuits

Download Microwave Integrated Circuits PDF Online Free

Author :
Publisher : CRC Press
ISBN 13 : 9780824781996
Total Pages : 628 pages
Book Rating : 4.7/5 (819 download)

DOWNLOAD NOW!


Book Synopsis Microwave Integrated Circuits by : Konishi

Download or read book Microwave Integrated Circuits written by Konishi and published by CRC Press. This book was released on 1991-03-29 with total page 628 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents to a wide range of students and engineers up-to-date techniques of MICs, with readily comprehensible explanations, providing a unified description of MICs, clarifying physical content, including sufficient data to be directly useful to active engineers, and providing a path of entry into th

VLSI Specification, Verification and Synthesis

Download VLSI Specification, Verification and Synthesis PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461320070
Total Pages : 405 pages
Book Rating : 4.4/5 (613 download)

DOWNLOAD NOW!


Book Synopsis VLSI Specification, Verification and Synthesis by : Graham Birtwistle

Download or read book VLSI Specification, Verification and Synthesis written by Graham Birtwistle and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 405 pages. Available in PDF, EPUB and Kindle. Book excerpt: VLSI Specification, Verification and Synthesis Proceedings of a workshop held in Calgary from 12-16 January 1987. The collection of papers in this book represents some of the discussions and presentations at a workshop on hardware verification held in Calgary, January 12-16 1987. The thrust of the workshop was to give the floor to a few leading researchers involved in the use of formal approaches to VLSI design, and provide them ample time to develop not only their latest ideas but also the evolution of these ideas. In contrast to simulation, where the objective is to assist in detecting errors in system behavior in the case of some selected inputs, the intent of hardware verification is to formally prove that a chip design meets a specification of its intended behavior (for all acceptable inputs). There are several important applications where formal verification of designs may be argued to be cost-effective. Examples include hardware components used in "safety critical" applications such as flight control, industrial plants, and medical life-support systems (such as pacemakers). The problems are of such magnitude in certain defense applications that the UK Ministry of Defense feels it cannot rely on commercial chips and has embarked on a program of producing formally verified chips to its own specification. Hospital, civil aviation, and transport boards in the UK will also use these chips. A second application domain for verification is afforded by industry where specific chips may be used in high volume or be remotely placed.

Control and Dynamic Systems V42: Analysis and Control System Techniques for Electric Power Systems Part 2

Download Control and Dynamic Systems V42: Analysis and Control System Techniques for Electric Power Systems Part 2 PDF Online Free

Author :
Publisher : Academic Press
ISBN 13 : 0323148735
Total Pages : 501 pages
Book Rating : 4.3/5 (231 download)

DOWNLOAD NOW!


Book Synopsis Control and Dynamic Systems V42: Analysis and Control System Techniques for Electric Power Systems Part 2 by : C.T. Leonides

Download or read book Control and Dynamic Systems V42: Analysis and Control System Techniques for Electric Power Systems Part 2 written by C.T. Leonides and published by Academic Press. This book was released on 2012-12-02 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: Control and Dynamic Systems: Advances in Theory and Applications, Volume 42: Analysis and Control System Techniques for Electric Power Systems, Part 2 of 4 covers the research studies on the significant advances in areas including economic operation of power systems and voltage and power control techniques. This book is composed of eight chapters and begins with a survey of the application of parallel processing to power system analysis as motivated by the requirement for faster computation. The next chapters deal with the issues of power system protection from a system point of view, the voltage stability phenomenon, and an overview of the techniques used in the reliability evaluation of large electric power systems. These chapters also look into the reliability assessment of bulk power systems, which are the composite of generation and high-voltage transmission, often called composite systems. These topics are followed by investigations of the potential of integer quadratic optimization to improve efficiency in a radial electric distribution system through the coordination of switched capacitors and regulators. Other chapters consider the issues of the optimal operation of a power system that are substantially complicated as a result of the large system scale nature of these issues. The final chapters explore the techniques for achieving requisite speed improvements that are essential to electric power systems and the problems on effective methods in hydro optimization. This book will be of value to electrical engineers, designers, and researchers.

Serial-Data Computation

Download Serial-Data Computation PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461320151
Total Pages : 246 pages
Book Rating : 4.4/5 (613 download)

DOWNLOAD NOW!


Book Synopsis Serial-Data Computation by : Stewart G. Smith

Download or read book Serial-Data Computation written by Stewart G. Smith and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 246 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is concerned with advances in serial-data computa tional architectures, and the CAD tools for their implementation in silicon. The bit-serial tradition at Edinburgh University (EU) stretches back some 6 years to the conception of the FIRST silicon compiler. FIRST owes much of its inspiration to Dick Lyon, then at Xerox P ARC, who proposed a 'structured-design' methodology for construction of signal processing systems from bit-serial building blocks. Based on an nMOS cell-library, FIRST automates much of Lyon's physical design process. More recently, we began to feel that FIRST should be able to exploit more modern technologies. Before this could be achieved, we were faced with a massive manual re-design task, i. e. the porting of FIRST cell-library to a new technology. As it was to avoid such tasks that FIRST was conceived in the first place, we decided to move the level of user-specification much nearer to the silicon level (while still hiding details of transistor circuit design, place and route etc. , from the user), and by so doing, enable the specification of more functionally powerful libraries in technology-free form. The results of this work are in evidence as advances in serial-data design techniques, and the SECOND silicon compiler, introduced later in this book. These achievements could not have been accomplished without help from various sources. We take this opportunity to thank Profs.

Silicon and Beyond

Download Silicon and Beyond PDF Online Free

Author :
Publisher : World Scientific
ISBN 13 : 9789810242800
Total Pages : 196 pages
Book Rating : 4.2/5 (428 download)

DOWNLOAD NOW!


Book Synopsis Silicon and Beyond by : Michael Shur

Download or read book Silicon and Beyond written by Michael Shur and published by World Scientific. This book was released on 2000 with total page 196 pages. Available in PDF, EPUB and Kindle. Book excerpt: The steady downscaling of device-feature size combined with a rapid increase in circuit complexity as well as the introduction of new device concepts based on non-silicon-material systems poses great challenges for device and circuit designers. One of the major tasks is the development of new and improved device models needed for accurate device and circuit design. Another task is the development of new circuit-simulation tools to handle very large and complex circuits. This book addresses both these issues with up-to-date reviews written by leading experts in the field. The first three chapters of the book discuss advanced device models both for existing technologies and for new, emerging technologies. Among the topics covered are models for MOSFETs, thin-film transitors (TFTs), and compound semiconductor devices, including GaAs HEMTs and HFETs, heterodimensional devices, quantum-tunneling devices, as well as wide-bandgap devices. Chapters 4 and 5 discuss advanced circuit simulators that hold promise for,handling circuits of much higher complexity than what is possible for typical state-of-the-art circuit simulators today.

Phonological Parsing in Speech Recognition

Download Phonological Parsing in Speech Recognition PDF Online Free

Author :
Publisher : Springer Science & Business Media
ISBN 13 : 1461320135
Total Pages : 272 pages
Book Rating : 4.4/5 (613 download)

DOWNLOAD NOW!


Book Synopsis Phonological Parsing in Speech Recognition by : K. Church

Download or read book Phonological Parsing in Speech Recognition written by K. Church and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: It is well-known that phonemes have different acoustic realizations depending on the context. Thus, for example, the phoneme /t! is typically realized with a heavily aspirated strong burst at the beginning of a syllable as in the word Tom, but without a burst at the end of a syllable in a word like cat. Variation such as this is often considered to be problematic for speech recogni tion: (1) "In most systems for sentence recognition, such modifications must be viewed as a kind of 'noise' that makes it more difficult to hypothesize lexical candidates given an in put phonetic transcription. To see that this must be the case, we note that each phonological rule [in a certain example] results in irreversible ambiguity-the phonological rule does not have a unique inverse that could be used to recover the underlying phonemic representation for a lexical item. For example, . . . schwa vowels could be the first vowel in a word like 'about' or the surface realization of almost any English vowel appearing in a sufficiently destressed word. The tongue flap [(] could have come from a /t! or a /d/. " [65, pp. 548-549] This view of allophonic variation is representative of much of the speech recognition literature, especially during the late 1970's. One can find similar statements by Cole and Jakimik [22] and by Jelinek [50].