VLSI CADhas greatly bene?ted from the use of reduced ordered Binary Decision Diagrams (BDDs) and the clausal representation as a problem of Boolean Satis?ability (SAT), e.g. in logic synthesis, ver- cation or design-for-testability. In recent practical applications, BDDs are optimized with respect to new objective functions for design space exploration. The latest trends show a growing number of proposals to fuse the concepts of BDD and SAT. This book gives a modern presentation of the established as well as of recent concepts. Latest results in BDD optimization are given, c- ering di?erent aspects of paths in BDDs and the use of e?cient lower bounds during optimization. The presented algorithms include Branch ? and Bound and the generic A -algorithm as e?cient techniques to - plore large search spaces. ? The A -algorithm originates from Arti?cial Intelligence (AI), and the EDA community has been unaware of this concept for a long time. Re- ? cently, the A -algorithm has been introduced as a new paradigm to explore design spaces in VLSI CAD. Besides AI search techniques, the book also discusses the relation to another ?eld of activity bordered to VLSI CAD and BDD optimization: the clausal representation as a SAT problem.

Advanced BDD Optimization

Computers & Technology

Drechsler, Rolf

Ebendt, Rudiger

Fey, Görschwin

Computer Science

Springer

Bridging the gap between elementary courses and the research literature in this field, the book covers the basic concepts necessary to study differential equations. Stability theory is developed, starting with linearisation methods going back to Lyapunov and Poincaré, before moving on to the global direct method. The Poincaré-Lindstedt method is introduced to approximate periodic solutions, while at the same time proving existence by the implicit function theorem. The final part covers relaxation oscillations, bifurcation theory, centre manifolds, chaos in mappings and differential equations, and Hamiltonian systems. The subject material is presented from both the qualitative and the quantitative point of view, with many examples to illustrate the theory, enabling the reader to begin research after studying this book.

Advanced BDD Optimization (Universitext)

Science & Math

Rudiger, Ebendt

Goerschwin, Fey

Mathematics

Spectral Techniques in VLSI CAD have become a subject of renewed interest in the design automation community due to the emergence of new and efficient methods for the computation of discrete function spectra. In the past, spectral computations for digital logic were too complex for practical implementation. The use of decision diagrams for spectral computations has greatly reduced this obstacle allowing for the development of new and useful spectral techniques for VLSI synthesis and verification. Several new algorithms for the computation of the Walsh, Reed-Muller, arithmetic and Haar spectra are described. The relation of these computational methods to traditional ones is also provided. Spectral Techniques in VLSI CAD provides a unified formalism of the representation of bit-level and word-level discrete functions in the spectral domain and as decision diagrams. An alternative and unifying interpretation of decision diagram representations is presented since it is shown that many of the different commonly used varieties of decision diagrams are merely graphical representations of various discrete function spectra. Viewing various decision diagrams as being described by specific sets of transformation functions not only illustrates the relationship between graphical and spectral representations of discrete functions, but also gives insight into how various decision diagram types are related. Spectral Techniques in VLSI CAD describes several new applications of spectral techniques in discrete function manipulation including decision diagram minimization, logic function synthesis, technology mapping and equivalence checking. The use of linear transformations in decision diagram size reduction is described and the relationship to the operation known as spectral translation is described. Several methods for synthesizing digital logic circuits based on a subset of spectral coefficients are described. An equivalence checking approach for functional verification is described based upon the use of matching pairs of Haar spectral coefficients.

Spectral Techniques in VLSI CAD

Miller, D. Michael

Thornton, Mitchell Aaron

The size of technically producible integrated circuits increases continuously, but the ability to design and verify these circuits does not keep up. Therefore today’s design flow has to be improved. Using a visionary approach, this book analyzes the current design methodology and verification methodology, a number of deficiencies are identified and solutions suggested. Improvements in the methodology as well as in the underlying algorithms are proposed.

Robustness and Usability in Modern Design Flows

The design process of digital circuits is often carried out in individual steps, like logic synthesis, mapping, and routing. Since originally the complete process was too complex, it has been split up in several - more or less independen- phases. In the last 40 years powerful algorithms have been developed to find optimal solutions for each of these steps. However, the interaction of these different algorithms has not been considered for a long time. This leads to quality loss e. g. in cases where highly optimized netlists fit badly onto the target architecture. Since the resulting circuits are often far from being optimal and insufficient regarding the optimization criteria, like area and delay, several iterations of the complete design process have to be carried out to get high quality results. This is a very time consuming and costly process. For this reason, some years ago the idea of one-pass synthesis came up. There were two main approaches how to guarantee that a design got "first time right" : 1. Combining levels that were split before, e. g. to use layout information already during the logic synthesis phase. 2. Restricting the optimization in one level such that it better fits to the next one. So far, several approaches in these two directions have been presented and new techniques are under development. In this book we describe the new paradigm that is used in one-pass synthesis and present examples for the two techniques above.

Towards One-Pass Synthesis

Günther, Wolfgang

VLSI CADhas greatly bene?ted from the use of reduced ordered Binary Decision Diagrams (BDDs) and the clausal representation as a problem of Boolean Satis?ability (SAT), e.g. in logic synthesis, ver- cation or design-for-testability. In recent practical applications, BDDs are optimized with respect to new objective functions for design space exploration. The latest trends show a growing number of proposals to fuse the concepts of BDD and SAT. This book gives a modern presentation of the established as well as of recent concepts. Latest results in BDD optimization are given, c- ering di?erent aspects of paths in BDDs and the use of e?cient lower bounds during optimization. The presented algorithms include Branch ? and Bound and the generic A -algorithm as e?cient techniques to - plore large search spaces. ? The A -algorithm originates from Arti?cial Intelligence (AI), and the EDA community has been unaware of this concept for a long time. Re- ? cently, the A -algorithm has been introduced as a new paradigm to explore design spaces in VLSI CAD. Besides AI search techniques, the book also discusses the relation to another ?eld of activity bordered to VLSI CAD and BDD optimization: the clausal representation as a SAT problem.

Formal verification has become one of the most important steps in circuit design. Since circuits can contain several million transistors, verification of such large designs becomes more and more difficult. Pure simulation cannot guarantee the correct behavior and exhaustive simulation is often impossible. However, many designs, like ALUs, have very regular structures that can be easily described at a higher level of abstraction. For example, describing (and verifying) an integer multiplier at the bit-level is very difficult, while the verification becomes easy when the outputs are grouped to build a bit-string. Recently, several approaches for formal circuit verification have been proposed that make use of these regularities. These approaches are based on Word-Level Decision Diagrams (WLDDs) which are graph-based representations of functions (similar to BDDs) that allow for the representation of functions with a Boolean range and an integer domain. Formal Verification of Circuits is devoted to the discussion of recent developments in the field of decision diagram-based formal verification. Firstly, different types of decision diagrams (including WLDDs) are introduced and theoretical properties are discussed that give further insight into the data structure. Secondly, implementation and minimization concepts are presented. Applications to arithmetic circuit verification and verification of designs specified by hardware description languages are described to show how WLDDs work in practice. Formal Verification of Circuits is intended for CAD developers and researchers as well as designers using modern verification tools. It will help people working with formal verification (in industry or academia) to keep informed about recent developments in this area.

Formal Verification of Circuits

The design process of digital circuits is often carried out in individual steps, like logic synthesis, mapping, and routing. Since originally the complete process was too complex, it has been split up in several - more or less independen- phases. In the last 40 years powerful algorithms have been developed to find optimal solutions for each of these steps. However, the interaction of these different algorithms has not been considered for a long time. This leads to quality loss e. g. in cases where highly optimized netlists fit badly onto the target architecture. Since the resulting circuits are often far from being optimal and insufficient regarding the optimization criteria, like area and delay, several iterations of the complete design process have to be carried out to get high quality results. This is a very time consuming and costly process. For this reason, some years ago the idea of one-pass synthesis came up. There were two main approaches how to guarantee that a design got "first time right" : 1. Combining levels that were split before, e. g. to use layout information already during the logic synthesis phase. 2. Restricting the optimization in one level such that it better fits to the next one. So far, several approaches in these two directions have been presented and new techniques are under development. In this book we describe the new paradigm that is used in one-pass synthesis and present examples for the two techniques above.

This book provides an overview of automatic test pattern generation (ATPG) and introduces novel techniques to complement classical ATPG, based on Boolean Satisfiability (SAT). A fast and highly fault efficient SAT-based ATPG framework is presented which is also able to generate high-quality delay tests such as robust path delay tests, as well as tests with long propagation paths to detect small delay defects.
The aim of the techniques and methodologies presented in this book is to improve SAT-based ATPG, in order to make it applicable in industrial practice. Readers will learn to improve the performance and robustness of the overall test generation process, so that the ATPG algorithm reliably will generate test patterns for most targeted faults in acceptable run time to meet the high fault coverage demands of industry. The techniques and improvements presented in this book provide the following advantages:
<ul>
<li>Provides a comprehensive introduction to test generation and Boolean Satisfiability (SAT);</li>
<li> Describes a highly fault efficient SAT-based ATPG framework; </li>
<li>Introduces circuit-oriented SAT solving techniques, which make use of structural information and are able to accelerate the search process significantly;</li>
<li>Provides SAT formulations for the prevalent delay faults models, in addition to the classical stuck-at fault model;</li>
<li>Includes an industrial perspective on the state-of-the-art in the testing, along with SAT; two topics typically distinguished from each other.</li>
</ul>

High Quality Test Pattern Generation and Boolean Satisfiability

Eggersglüß, Stephan

Spectral Techniques in VLSI CAD have become a subject of renewed interest in the design automation community due to the emergence of new and efficient methods for the computation of discrete function spectra. In the past, spectral computations for digital logic were too complex for practical implementation. The use of decision diagrams for spectral computations has greatly reduced this obstacle allowing for the development of new and useful spectral techniques for VLSI synthesis and verification. Several new algorithms for the computation of the Walsh, Reed-Muller, arithmetic and Haar spectra are described. The relation of these computational methods to traditional ones is also provided. Spectral Techniques in VLSI CAD provides a unified formalism of the representation of bit-level and word-level discrete functions in the spectral domain and as decision diagrams. An alternative and unifying interpretation of decision diagram representations is presented since it is shown that many of the different commonly used varieties of decision diagrams are merely graphical representations of various discrete function spectra. Viewing various decision diagrams as being described by specific sets of transformation functions not only illustrates the relationship between graphical and spectral representations of discrete functions, but also gives insight into how various decision diagram types are related. Spectral Techniques in VLSI CAD describes several new applications of spectral techniques in discrete function manipulation including decision diagram minimization, logic function synthesis, technology mapping and equivalence checking. The use of linear transformations in decision diagram size reduction is described and the relationship to the operation known as spectral translation is described. Several methods for synthesizing digital logic circuits based on a subset of spectral coefficients are described. An equivalence checking approach for functional verification is described based upon the use of matching pairs of Haar spectral coefficients.

See the best price to sell, buy, or rent books by Drechsler, Rolf. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Books by Drechsler, Rolf

See the best price to sell, buy, or rent books by Drechsler, Rolf. BookScouter helps to compare book prices from 25+ online bookstores and 30+ buyback vendors with a single search.

Advanced BDD Optimization

Advanced BDD Optimization (Universitext)

Spectral Techniques in VLSI CAD

Robustness and Usability in Modern Design Flows

Towards One-Pass Synthesis

Advanced BDD Optimization

Formal Verification of Circuits

Towards One-Pass Synthesis

High Quality Test Pattern Generation and Boolean Satisfiability

Spectral Techniques in VLSI CAD