Arithmetic Circuits

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Arithmetic Circuits

Author : Amir Shpilka
Publisher : Now Publishers Inc
ISBN 13 : 1601984006
Total Pages : 193 pages
Book Rating : 4.6/5 (19 download)

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Book Synopsis Arithmetic Circuits by : Amir Shpilka

Download or read book Arithmetic Circuits written by Amir Shpilka and published by Now Publishers Inc. This book was released on 2010 with total page 193 pages. Available in PDF, EPUB and Kindle. Book excerpt: A large class of problems in symbolic computation can be expressed as the task of computing some polynomials; and arithmetic circuits form the most standard model for studying the complexity of such computations. This algebraic model of computation attracted a large amount of research in the last five decades, partially due to its simplicity and elegance. Being a more structured model than Boolean circuits, one could hope that the fundamental problems of theoretical computer science, such as separating P from NP, will be easier to solve for arithmetic circuits. However, in spite of the appearing simplicity and the vast amount of mathematical tools available, no major breakthrough has been seen. In fact, all the fundamental questions are still open for this model as well. Nevertheless, there has been a lot of progress in the area and beautiful results have been found, some in the last few years. As examples we mention the connection between polynomial identity testing and lower bounds of Kabanets and Impagliazzo, the lower bounds of Raz for multilinear formulas, and two new approaches for proving lower bounds: Geometric Complexity Theory and Elusive Functions. The goal of this monograph is to survey the field of arithmetic circuit complexity, focusing mainly on what we find to be the most interesting and accessible research directions. We aim to cover the main results and techniques, with an emphasis on works from the last two decades. In particular, we discuss the recent lower bounds for multilinear circuits and formulas, the advances in the question of deterministically checking polynomial identities, and the results regarding reconstruction of arithmetic circuits. We do, however, also cover part of the classical works on arithmetic circuits. In order to keep this monograph at a reasonable length, we do not give full proofs of most theorems, but rather try to convey the main ideas behind each proof and demonstrate it, where possible, by proving some special cases.

Synthesis of Arithmetic Circuits

Author : Jean-Pierre Deschamps
Publisher : John Wiley & Sons
ISBN 13 : 0471741418
Total Pages : 578 pages
Book Rating : 4.4/5 (717 download)

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Book Synopsis Synthesis of Arithmetic Circuits by : Jean-Pierre Deschamps

Download or read book Synthesis of Arithmetic Circuits written by Jean-Pierre Deschamps and published by John Wiley & Sons. This book was released on 2006-03-24 with total page 578 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to the study of arithmetic circuits In Synthesis of Arithmetic Circuits: FPGA, ASIC and Embedded Systems, the authors take a novel approach of presenting methods and examples for the synthesis of arithmetic circuits that better reflects the needs of today's computer system designers and engineers. Unlike other publications that limit discussion to arithmetic units for general-purpose computers, this text features a practical focus on embedded systems. Following an introductory chapter, the publication is divided into two parts. The first part, Mathematical Aspects and Algorithms, includes mathematical background, number representation, addition and subtraction, multiplication, division, other arithmetic operations, and operations in finite fields. The second part, Synthesis of Arithmetic Circuits, includes hardware platforms, general principles of synthesis, adders and subtractors, multipliers, dividers, and other arithmetic primitives. In addition, the publication distinguishes itself with: * A separate treatment of algorithms and circuits-a more useful presentation for both software and hardware implementations * Complete executable and synthesizable VHDL models available on the book's companion Web site, allowing readers to generate synthesizable descriptions * Proposed FPGA implementation examples, namely synthesizable low-level VHDL models for the Spartan II and Virtex families * Two chapters dedicated to finite field operations This publication is a must-have resource for students in computer science and embedded system designers, engineers, and researchers in the field of hardware and software computer system design and development. An Instructor Support FTP site is available from the Wiley editorial department.

Arithmetic Circuits for DSP Applications

Author : Pramod Kumar Meher
Publisher : John Wiley & Sons
ISBN 13 : 1119206774
Total Pages : 342 pages
Book Rating : 4.1/5 (192 download)

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Book Synopsis Arithmetic Circuits for DSP Applications by : Pramod Kumar Meher

Download or read book Arithmetic Circuits for DSP Applications written by Pramod Kumar Meher and published by John Wiley & Sons. This book was released on 2017-10-03 with total page 342 pages. Available in PDF, EPUB and Kindle. Book excerpt: A comprehensive guide to the fundamental concepts, designs, and implementation schemes, performance considerations, and applications of arithmetic circuits for DSP Arithmetic Circuits for DSP Applications is a complete resource on arithmetic circuits for digital signal processing (DSP). It covers the key concepts, designs and developments of different types of arithmetic circuits, which can be used for improving the efficiency of implementation of a multitude of DSP applications. Each chapter includes various applications of the respective class of arithmetic circuits along with information on the future scope of research. Written for students, engineers, and researchers in electrical and computer engineering, this comprehensive text offers a clear understanding of different types of arithmetic circuits used for digital signal processing applications. The text includes contributions from noted researchers on a wide range of topics, including a review of circuits used in implementing basic operations like additions and multiplications; distributed arithmetic as a technique for the multiplier-less implementation of inner products for DSP applications; discussions on look up table-based techniques and their key applications; CORDIC circuits for calculation of trigonometric, hyperbolic and logarithmic functions; real and complex multiplications, division, and square-root; solution of linear systems; eigenvalue estimation; singular value decomposition; QR factorization and many other functions through the use of simple shift-add operations; and much more. This book serves as a comprehensive resource, which describes the arithmetic circuits as fundamental building blocks for state-of-the-art DSP and reviews in - depth the scope of their applications.

Arithmetic and Algebraic Circuits

Author : Antonio Lloris Ruiz
Publisher : Springer Nature
ISBN 13 : 3030672662
Total Pages : 682 pages
Book Rating : 4.0/5 (36 download)

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Book Synopsis Arithmetic and Algebraic Circuits by : Antonio Lloris Ruiz

Download or read book Arithmetic and Algebraic Circuits written by Antonio Lloris Ruiz and published by Springer Nature. This book was released on 2021-03-27 with total page 682 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a complete and accurate study of arithmetic and algebraic circuits. The first part offers a review of all important basic concepts: it describes simple circuits for the implementation of some basic arithmetic operations; it introduces theoretical basis for residue number systems; and describes some fundamental circuits for implementing the main modular operations that will be used in the text. Moreover, the book discusses floating-point representation of real numbers and the IEEE 754 standard. The second and core part of the book offers a deep study of arithmetic circuits and specific algorithms for their implementation. It covers the CORDIC algorithm, and optimized arithmetic circuits recently developed by the authors for adders and subtractors, as well as multipliers, dividers and special functions. It describes the implementation of basic algebraic circuits, such as LFSRs and cellular automata. Finally, it offers a complete study of Galois fields, showing some exemplary applications and discussing the advantages in comparison to other methods. This dense, self-contained text provides students, researchers and engineers, with extensive knowledge on and a deep understanding of arithmetic and algebraic circuits and their implementation.

Digital Electronics 2

Author : Tertulien Ndjountche
Publisher : John Wiley & Sons
ISBN 13 : 1848219857
Total Pages : 328 pages
Book Rating : 4.8/5 (482 download)

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Book Synopsis Digital Electronics 2 by : Tertulien Ndjountche

Download or read book Digital Electronics 2 written by Tertulien Ndjountche and published by John Wiley & Sons. This book was released on 2016-08-29 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: As electronic devices become increasingly prevalent in everyday life, digital circuits are becoming even more complex and smaller in size. This book presents the basic principles of digital electronics in an accessible manner, allowing the reader to grasp the principles of combinational and sequential logic and the underlying techniques for the analysis and design of digital circuits. Providing a hands-on approach, this work introduces techniques and methods for establishing logic equations and designing and analyzing digital circuits. Each chapter is supplemented with practical examples and well-designed exercises with worked solutions. This second of three volumes focuses on sequential and arithmetic logic circuits. It covers various aspects related to the following topics: latch and flip-flop; binary counters; shift registers; arithmetic and logic circuits; digital integrated circuit technology; semiconductor memory; programmable logic circuits. Along with the two accompanying volumes, this book is an indispensable tool for students at a bachelors or masters level seeking to improve their understanding of digital electronics, and is detailed enough to serve as a reference for electronic, automation and computer engineers.

Algebraic Circuits

Author : Antonio Lloris Ruiz
Publisher : Springer Science & Business Media
ISBN 13 : 3642546498
Total Pages : 413 pages
Book Rating : 4.6/5 (425 download)

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Book Synopsis Algebraic Circuits by : Antonio Lloris Ruiz

Download or read book Algebraic Circuits written by Antonio Lloris Ruiz and published by Springer Science & Business Media. This book was released on 2014-04-05 with total page 413 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a complete and accurate study of algebraic circuits, digital circuits whose performance can be associated with any algebraic structure. The authors distinguish between basic algebraic circuits, such as Linear Feedback Shift Registers (LFSRs) and cellular automata and algebraic circuits, such as finite fields or Galois fields. The book includes a comprehensive review of representation systems, of arithmetic circuits implementing basic and more complex operations and of the residue number systems (RNS). It presents a study of basic algebraic circuits such as LFSRs and cellular automata as well as a study of circuits related to Galois fields, including two real cryptographic applications of Galois fields.

Guide to FPGA Implementation of Arithmetic Functions

Author : Jean-Pierre Deschamps
Publisher : Springer Science & Business Media
ISBN 13 : 9400729863
Total Pages : 473 pages
Book Rating : 4.4/5 (7 download)

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Book Synopsis Guide to FPGA Implementation of Arithmetic Functions by : Jean-Pierre Deschamps

Download or read book Guide to FPGA Implementation of Arithmetic Functions written by Jean-Pierre Deschamps and published by Springer Science & Business Media. This book was released on 2012-04-05 with total page 473 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is designed both for FPGA users interested in developing new, specific components - generally for reducing execution times –and IP core designers interested in extending their catalog of specific components. The main focus is circuit synthesis and the discussion shows, for example, how a given algorithm executing some complex function can be translated to a synthesizable circuit description, as well as which are the best choices the designer can make to reduce the circuit cost, latency, or power consumption. This is not a book on algorithms. It is a book that shows how to translate efficiently an algorithm to a circuit, using techniques such as parallelism, pipeline, loop unrolling, and others. Numerous examples of FPGA implementation are described throughout this book and the circuits are modeled in VHDL. Complete and synthesizable source files are available for download.

Design of Arithmetic Circuits in Quantum Dot Cellular Automata Nanotechnology

Author : K. Sridharan
Publisher : Springer
ISBN 13 : 3319166883
Total Pages : 122 pages
Book Rating : 4.3/5 (191 download)

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Book Synopsis Design of Arithmetic Circuits in Quantum Dot Cellular Automata Nanotechnology by : K. Sridharan

Download or read book Design of Arithmetic Circuits in Quantum Dot Cellular Automata Nanotechnology written by K. Sridharan and published by Springer. This book was released on 2015-03-26 with total page 122 pages. Available in PDF, EPUB and Kindle. Book excerpt: This research monograph focuses on the design of arithmetic circuits in Quantum Dot Cellular Automata (QCA). Using the fact that the 3-input majority gate is a primitive in QCA, the book sets out to discover hitherto unknown properties of majority logic in the context of arithmetic circuit designs. The pursuit for efficient adders in QCA takes two forms. One involves application of the new results in majority logic to existing adders. The second involves development of a custom adder for QCA technology. A QCA adder named as hybrid adder is proposed and it is shown that it outperforms existing multi-bit adders with respect to area and delay. The work is extended to the design of a low-complexity multiplier for signed numbers in QCA. Furthermore the book explores two aspects unique to QCA technology, namely thermal robustness and the role of interconnects. In addition, the book introduces the reader to QCA layout design and simulation using QCADesigner. Features & Benefits: This research-based book: ·Introduces the reader to Quantum Dot Cellular Automata, an emerging nanotechnology. ·Explores properties of majority logic. ·Demonstrates application of the properties to design efficient arithmetic circuits. ·Guides the reader towards layout design and simulation in QCADesigner.

Approximate Computing

Author : Weiqiang Liu
Publisher : Springer Nature
ISBN 13 : 3030983471
Total Pages : 607 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Approximate Computing by : Weiqiang Liu

Download or read book Approximate Computing written by Weiqiang Liu and published by Springer Nature. This book was released on 2022-08-22 with total page 607 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book explores the technological developments at various levels of abstraction, of the new paradigm of approximate computing. The authors describe in a single-source the state-of-the-art, covering the entire spectrum of research activities in approximate computing, bridging device, circuit, architecture, and system levels. Content includes tutorials, reviews and surveys of current theoretical/experimental results, design methodologies and applications developed in approximate computing for a wide scope of readership and specialists. Serves as a single-source reference to state-of-the-art of approximate computing; Covers broad range of topics, from circuits to applications; Includes contributions by leading researchers, from academia and industry.

Automata, Languages and Programming

Author : Luca Aceto
Publisher : Springer
ISBN 13 : 3642220061
Total Pages : 825 pages
Book Rating : 4.6/5 (422 download)

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Book Synopsis Automata, Languages and Programming by : Luca Aceto

Download or read book Automata, Languages and Programming written by Luca Aceto and published by Springer. This book was released on 2011-06-21 with total page 825 pages. Available in PDF, EPUB and Kindle. Book excerpt: The two-volume set LNCS 6755 and LNCS 6756 constitutes the refereed proceedings of the 38th International Colloquium on Automata, Languages and Programming, ICALP 2011, held in Zürich, Switzerland, in July 2011. The 114 revised full papers (68 papers for track A, 29 for track B, and 17 for track C) presented together with 4 invited talks, 3 best student papers, and 3 best papers were carefully reviewed and selected from a total of 398 submissions. The papers are grouped in three major tracks on algorithms, complexity and games; on logic, semantics, automata, and theory of programming; as well as on foundations of networked computation: models, algorithms and information management.

Fundamentals of Computation Theory

Author : Ralf Klasing
Publisher : Springer
ISBN 13 : 3662557517
Total Pages : 448 pages
Book Rating : 4.6/5 (625 download)

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Book Synopsis Fundamentals of Computation Theory by : Ralf Klasing

Download or read book Fundamentals of Computation Theory written by Ralf Klasing and published by Springer. This book was released on 2017-08-28 with total page 448 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the refereed proceedings of the 21st International Symposium on Fundamentals of Computation Theory, FCT 2017, held in Bordeaux, France, in September 2017. The 29 revised full papers and 5 invited papers presented were carefully reviewed and selected from 99 submissions. The papers cover topics of all aspects of theoretical computer science, in particular algorithms, complexity, formal and logical methods.

Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques

Author : Maria Serna
Publisher : Springer Science & Business Media
ISBN 13 : 3642153682
Total Pages : 794 pages
Book Rating : 4.6/5 (421 download)

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Book Synopsis Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques by : Maria Serna

Download or read book Approximation, Randomization, and Combinatorial Optimization. Algorithms and Techniques written by Maria Serna and published by Springer Science & Business Media. This book was released on 2010-08-19 with total page 794 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book constitutes the joint refereed proceedings of the 13th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems, APPROX 2010, and the 14th International Workshop on Randomization and Computation, RANDOM 2010, held in Barcelona, Spain, in September 2010. The 28 revised full papers of the APPROX 2010 workshop and the 29 revised full papers of the RANDOM 2010 workshop included in this volume, were carefully reviewed and selected from 66 and 61 submissions, respectively. APPROX focuses on algorithmic and complexity issues surrounding the development of efficient approximate solutions to computationally difficult problems. RANDOM is concerned with applications of randomness to computational and combinatorial problems.

Tropical Circuit Complexity

Author : Stasys Jukna
Publisher : Springer Nature
ISBN 13 : 3031423542
Total Pages : 138 pages
Book Rating : 4.0/5 (314 download)

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Book Synopsis Tropical Circuit Complexity by : Stasys Jukna

Download or read book Tropical Circuit Complexity written by Stasys Jukna and published by Springer Nature. This book was released on 2023-12-08 with total page 138 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents an enticing introduction to tropical circuits and their use as a rigorous mathematical model for dynamic programming (DP), which is one of the most fundamental algorithmic paradigms for solving combinatorial, discrete optimization problems. In DP, an optimization problem is broken up into smaller subproblems that are solved recursively. Many classical DP algorithms are pure in that they only use the basic (min,+) or (max,+) operations in their recursion equations. In tropical circuits, these operations are used as gates. Thanks to the rigorous combinatorial nature of tropical circuits, elements from the Boolean and arithmetic circuit complexity can be used to obtain lower bounds for tropical circuits, which play a crucial role in understanding the limitations and capabilities of these computational models. This book aims to offer a toolbox for proving lower bounds on the size of tropical circuits. In this work, the reader will find lower-bound ideas and methods that have emerged in the last few years, with detailed proofs. Largely self-contained, this book is meant to be approachable by graduate students in mathematics and computer science with a special interest in circuit complexity.

Computers, Software Engineering, and Digital Devices

Author : Richard C. Dorf
Publisher : CRC Press
ISBN 13 : 1420037056
Total Pages : 576 pages
Book Rating : 4.4/5 (2 download)

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Book Synopsis Computers, Software Engineering, and Digital Devices by : Richard C. Dorf

Download or read book Computers, Software Engineering, and Digital Devices written by Richard C. Dorf and published by CRC Press. This book was released on 2018-10-03 with total page 576 pages. Available in PDF, EPUB and Kindle. Book excerpt: In two editions spanning more than a decade, The Electrical Engineering Handbook stands as the definitive reference to the multidisciplinary field of electrical engineering. Our knowledge continues to grow, and so does the Handbook. For the third edition, it has expanded into a set of six books carefully focused on a specialized area or field of study. Each book represents a concise yet definitive collection of key concepts, models, and equations in its respective domain, thoughtfully gathered for convenient access. Computers, Software Engineering, and Digital Devices examines digital and logical devices, displays, testing, software, and computers, presenting the fundamental concepts needed to ensure a thorough understanding of each field. It treats the emerging fields of programmable logic, hardware description languages, and parallel computing in detail. Each article includes defining terms, references, and sources of further information. Encompassing the work of the world's foremost experts in their respective specialties, Computers, Software Engineering, and Digital Devices features the latest developments, the broadest scope of coverage, and new material on secure electronic commerce and parallel computing.

Circuit Design with VHDL, third edition

Author : Volnei A. Pedroni
Publisher : MIT Press
ISBN 13 : 0262042649
Total Pages : 609 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Circuit Design with VHDL, third edition by : Volnei A. Pedroni

Download or read book Circuit Design with VHDL, third edition written by Volnei A. Pedroni and published by MIT Press. This book was released on 2020-04-14 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: A completely updated and expanded comprehensive treatment of VHDL and its applications to the design and simulation of real, industry-standard circuits. This comprehensive treatment of VHDL and its applications to the design and simulation of real, industry-standard circuits has been completely updated and expanded for the third edition. New features include all VHDL-2008 constructs, an extensive review of digital circuits, RTL analysis, and an unequaled collection of VHDL examples and exercises. The book focuses on the use of VHDL rather than solely on the language, with an emphasis on design examples and laboratory exercises. The third edition begins with a detailed review of digital circuits (combinatorial, sequential, state machines, and FPGAs), thus providing a self-contained single reference for the teaching of digital circuit design with VHDL. In its coverage of VHDL-2008, it makes a clear distinction between VHDL for synthesis and VHDL for simulation. The text offers complete VHDL codes in examples as well as simulation results and comments. The significantly expanded examples and exercises include many not previously published, with multiple physical demonstrations meant to inspire and motivate students. The book is suitable for undergraduate and graduate students in VHDL and digital circuit design, and can be used as a professional reference for VHDL practitioners. It can also serve as a text for digital VLSI in-house or academic courses.

Neuro-Symbolic Artificial Intelligence: The State of the Art

Author : P. Hitzler
Publisher : IOS Press
ISBN 13 : 1643682458
Total Pages : 410 pages
Book Rating : 4.6/5 (436 download)

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Book Synopsis Neuro-Symbolic Artificial Intelligence: The State of the Art by : P. Hitzler

Download or read book Neuro-Symbolic Artificial Intelligence: The State of the Art written by P. Hitzler and published by IOS Press. This book was released on 2022-01-19 with total page 410 pages. Available in PDF, EPUB and Kindle. Book excerpt: Neuro-symbolic AI is an emerging subfield of Artificial Intelligence that brings together two hitherto distinct approaches. ”Neuro” refers to the artificial neural networks prominent in machine learning, ”symbolic” refers to algorithmic processing on the level of meaningful symbols, prominent in knowledge representation. In the past, these two fields of AI have been largely separate, with very little crossover, but the so-called “third wave” of AI is now bringing them together. This book, Neuro-Symbolic Artificial Intelligence: The State of the Art, provides an overview of this development in AI. The two approaches differ significantly in terms of their strengths and weaknesses and, from a cognitive-science perspective, there is a question as to how a neural system can perform symbol manipulation, and how the representational differences between these two approaches can be bridged. The book presents 17 overview papers, all by authors who have made significant contributions in the past few years and starting with a historic overview first seen in 2016. With just seven months elapsed from invitation to authors to final copy, the book is as up-to-date as a published overview of this subject can be. Based on the editors’ own desire to understand the current state of the art, this book reflects the breadth and depth of the latest developments in neuro-symbolic AI, and will be of interest to students, researchers, and all those working in the field of Artificial Intelligence.

Mathematical Foundations of Computer Science 2015

Author : Giuseppe F. Italiano
Publisher : Springer
ISBN 13 : 3662480549
Total Pages : 633 pages
Book Rating : 4.6/5 (624 download)

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Book Synopsis Mathematical Foundations of Computer Science 2015 by : Giuseppe F. Italiano

Download or read book Mathematical Foundations of Computer Science 2015 written by Giuseppe F. Italiano and published by Springer. This book was released on 2015-08-10 with total page 633 pages. Available in PDF, EPUB and Kindle. Book excerpt: This two volume set LNCS 9234 and 9235 constitutes the refereed conference proceedings of the 40th International Symposium on Mathematical Foundations of Computer Science, MFCS 2015, held in Milan, Italy, in August 2015. The 82 revised full papers presented together with 5 invited talks were carefully selected from 201 submissions. The papers feature high-quality research in all branches of theoretical computer science. They have been organized in the following topical main sections: logic, semantics, automata, and theory of programming (volume 1) and algorithms, complexity, and games (volume 2).