During the development of digital circuits, their functional correctness has to be ensured, for which formal verification methods have been established. However, the verification process using formal methods can have an exponential time or space complexity, causing the verification to fail. While exponential in general, recently it has been proven that the verification complexity of several circuits is polynomially bounded. Martha Schnieber proves the polynomial verifiability of several approximate circuits, which are beneficial in error-tolerant applications, where the circuit approximates the exact function in some cases, while having a lower delay or being more area-efficient. Here, upper bounds for the BDD size and the time and space complexity are provided for the verification of general approximate functions and several state-of-the-art approximate adders.
This book presents 8 papers accompanying the lectures of leading researchers given at the 6th edition of the International School on Formal Methods for the Design of Computer, Communication and Software Systems (SFM 2006). SFM 2006 was devoted to formal techniques for hardware verification and covers several aspects of the hardware design process, including hardware design languages and simulation, property specification formalisms, automatic test pattern generation, symbolic trajectory evaluation, and more.
Over seventy years ago, Richard Bellman coined the term “the curse of dimensionality” to describe phenomena and computational challenges that arise in high dimensions. These challenges, in tandem with the ubiquity of high-dimensional functions in real-world applications, have led to a lengthy, focused research effort on high-dimensional approximation—that is, the development of methods for approximating functions of many variables accurately and efficiently from data. This book provides an in-depth treatment of one of the latest installments in this long and ongoing story: sparse polynomial approximation methods. These methods have emerged as useful tools for various high-dimensional approximation tasks arising in a range of applications in computational science and engineering. It begins with a comprehensive overview of best s-term polynomial approximation theory for holomorphic, high-dimensional functions, as well as a detailed survey of applications to parametric differential equations. It then describes methods for computing sparse polynomial approximations, focusing on least squares and compressed sensing techniques. Sparse Polynomial Approximation of High-Dimensional Functions presents the first comprehensive and unified treatment of polynomial approximation techniques that can mitigate the curse of dimensionality in high-dimensional approximation, including least squares and compressed sensing. It develops main concepts in a mathematically rigorous manner, with full proofs given wherever possible, and it contains many numerical examples, each accompanied by downloadable code. The authors provide an extensive bibliography of over 350 relevant references, with an additional annotated bibliography available on the book’s companion website (www.sparse-hd-book.com). This text is aimed at graduate students, postdoctoral fellows, and researchers in mathematics, computer science, and engineering who are interested in high-dimensional polynomial approximation techniques.
This volume contains the proceedings of the Fourth Biennial Conference on F- mal Methods in Computer-Aided Design (FMCAD). The conference is devoted to the use of mathematical methods for the analysis of digital hardware c- cuits and systems. The workreported in this bookdescribes the use of formal mathematics and associated tools to design and verify digital hardware systems. Functional veri?cation has become one of the principal costs in a modern computer design e?ort. FMCAD provides a venue for academic and industrial researchers and practitioners to share their ideas and experiences of using - screte mathematical modeling and veri?cation. Over the past 20 years, this area has grown from just a few academic researchers to a vibrant worldwide com- nity of people from both academia and industry. This volume includes 23 papers selected from the 47 submitted papers, each of which was reviewed by at least three program committee members. The history of FMCAD dates backto 1984, when the earliest meetings on this topic occurred as part of IFIP WG10.2.
This book constitutes the proceedings of the 15th International Symposium on NASA Formal Methods, NFM 2023, held in Houston, Texas, USA, during May 16-18, 2023. The 26 full and 3 short papers presented in this volume were carefully reviewed and selected from 75 submissions. The papers deal with advances in formal methods, formal methods techniques, and formal methods in practice.
Illustrated with real-life manufacturing examples, Formal Methods in Manufacturing provides state-of-the-art solutions to common problems in manufacturing systems. Assuming some knowledge of discrete event systems theory, the book first delivers a detailed introduction to the most important formalisms used for the modeling, analysis, and control of manufacturing systems (including Petri nets, automata, and max-plus algebra), explaining the advantages of each formal method. It then employs the different formalisms to solve specific problems taken from today’s industrial world, such as modeling and simulation, supervisory control (including deadlock prevention) in a distributed and/or decentralized environment, performance evaluation (including scheduling and optimization), fault diagnosis and diagnosability analysis, and reconfiguration. Containing chapters written by leading experts in their respective fields, Formal Methods in Manufacturing helps researchers and application engineers handle fundamental principles and deal with typical quality goals in the design and operation of manufacturing systems.
This book constitutes the refereed proceedings of the Fourth International Symposium on NASA Formal Methods, NFM 2012, held in Norfolk, VA, USA, in April 2012. The 36 revised regular papers presented together with 10 short papers, 3 invited talks were carefully reviewed and selected from 93 submissions. The topics are organized in topical sections on theorem proving, symbolic execution, model-based engineering, real-time and stochastic systems, model checking, abstraction and abstraction refinement, compositional verification techniques, static and dynamic analysis techniques, fault protection, cyber security, specification formalisms, requirements analysis and applications of formal techniques.
