Formal Verification Of Circuits
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Formal Verification of Circuits
Author: Rolf Drechsler
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-03-09
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.
Applied Formal Verification
Author: Douglas L. Perry
language: en
Publisher: McGraw Hill Professional
Release Date: 2005-05-10
Formal verification is a powerful new digital design method. In this cutting-edge tutorial, two of the field's best known authors team up to show designers how to efficiently apply Formal Verification, along with hardware description languages like Verilog and VHDL, to more efficiently solve real-world design problems. Contents: Simulation-Based Verification * Introduction to Formal Techniques * Contrasting Simulation vs. Formal Techniques * Developing a Formal Test Plan * Writing High-Level Requirements * Proving High-Level Requirements * System Level Simulation * Design Example * Formal Test Plan * Final System Simulation
Formal Verification of Floating-Point Hardware Design
This is the first book to focus on the problem of ensuring the correctness of floating-point hardware designs through mathematical methods. Formal Verification of Floating-Point Hardware Design advances a verification methodology based on a unified theory of register-transfer logic and floating-point arithmetic that has been developed and applied to the formal verification of commercial floating-point units over the course of more than two decades, during which the author was employed by several major microprocessor design companies. The book consists of five parts, the first two of which present a rigorous exposition of the general theory based on the first principles of arithmetic. Part I covers bit vectors and the bit manipulation primitives, integer and fixed-point encodings, and bit-wise logical operations. Part II addresses the properties of floating-point numbers, the formats in which they are encoded as bit vectors, and the various modes of floating-point rounding. In Part III, the theory is extended to the analysis of several algorithms and optimization techniques that are commonly used in commercial implementations of elementary arithmetic operations. As a basis for the formal verification of such implementations, Part IV contains high-level specifications of correctness of the basic arithmetic instructions of several major industry-standard floating-point architectures, including all details pertaining to the handling of exceptional conditions. Part V illustrates the methodology, applying the preceding theory to the comprehensive verification of a state-of-the-art commercial floating-point unit. All of these results have been formalized in the logic of the ACL2 theorem prover and mechanically checked to ensure their correctness. They are presented here, however, in simple conventional mathematical notation. The book presupposes no familiarity with ACL2, logic design, or any mathematics beyond basic high school algebra. It will be of interest to verification engineers as well as arithmetic circuit designers who appreciate the value of a rigorous approach to their art, and is suitable as a graduate text in computer arithmetic.