Showing posts with label Theory of Computing. Show all posts
Showing posts with label Theory of Computing. Show all posts

Tuesday, March 8, 2011

Computer Science Logic: 7th Workshop, CSL '93, Swansea, United Kingdom, September 13 - 17, 1993. Selected Papers (Lecture Notes in Computer Science)



Computer Science Logic: 7th Workshop, CSL '93, Swansea, United Kingdom, September 13 - 17, 1993. Selected Papers (Lecture Notes in Computer Science)
Egon Börger,Yuri Gurevich,Karl Meinke | 1994-08-26 00:00:00 | Springer | 336 | Theory of Computing
This volume contains the final versions of a collection of papers presented at the Annual Conference of the European Association for Computer Science Logic, CSL '93, held at Swansea, UK in September 1993.
The 21 full papers included were selected from a total of 62 submissions and essentially contribute to the whole area of computer science logic research. They are devoted to such topics as set constraints, lambda calculi, process algebras, program semantics, intuitionistic logics, fixed-point logics, the equivalence problem, Horn clauses, quantifiers, and proof tranformations.

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Saturday, February 19, 2011

Logic for Programming, Artificial Intelligence, and Reasoning: 14th International Conference, LPAR 2007, Yerevan, Armenia, October 15-19, 2007, Proceedings ... / Lecture Notes in Artificial Intelligence)



Logic for Programming, Artificial Intelligence, and Reasoning: 14th International Conference, LPAR 2007, Yerevan, Armenia, October 15-19, 2007, Proceedings ... / Lecture Notes in Artificial Intelligence)
Nachum Dershowitz,Andrei Voronkov | 2007-12-12 00:00:00 | Springer | 562 | Theory of Computing

This book constitutes the refereed proceedings of the 14th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning, LPAR 2007, held in Yerevan, Armenia, October 15-19, 2007.

The 36 revised full papers presented together with 15 short papers and 3 invited talks were carefully reviewed and selected from 78 submissions. The papers address all current issues in logic programming, logic-based program manipulation, formal method, automated reasoning, and various kinds of AI logics.



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Monday, January 24, 2011

Algorithms for Memory Hierarchies: Advanced Lectures (Lecture Notes in Computer Science)



Algorithms for Memory Hierarchies: Advanced Lectures (Lecture Notes in Computer Science)
Ulrich Meyer,Peter Sanders,Jop Sibeyn | 2003-07-29 00:00:00 | Springer | 428 | Theory of Computing

Algorithms that have to process large data sets have to take into account that the cost of memory access depends on where the data is stored. Traditional algorithm design is based on the von Neumann model where accesses to memory have uniform cost. Actual machines increasingly deviate from this model: while waiting for memory access, nowadays, microprocessors can in principle execute 1000 additions of registers; for hard disk access this factor can reach six orders of magnitude.

The 16 coherent chapters in this monograph-like tutorial book introduce and survey algorithmic techniques used to achieve high performance on memory hierarchies; emphasis is placed on methods interesting from a theoretical as well as important from a practical point of view.

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Wednesday, January 12, 2011

Algebraic Complexity Theory (Grundlehren der mathematischen Wissenschaften)



Algebraic Complexity Theory (Grundlehren der mathematischen Wissenschaften)
Peter Bürgisser,Michael Clausen,Mohammad A. Shokrollahi | 1997-02-14 00:00:00 | Springer | 618 | Theory of Computing
This is the first book to present an up-to-date and self-contained account of Algebraic Complexity Theory that is both comprehensive and unified. Requiring of the reader only some basic algebra and offering over 350 exercises, it is well-suited as a textbook for beginners at graduate level. With its extensive bibliography covering about 500 research papers, this text is also an ideal reference book for the professional researcher. The subdivision of the contents into 21 more or less independent chapters enables readers to familiarize themselves quickly with a specific topic, and facilitates the use of this book as a basis for complementary courses in other areas such as computer algebra.
Reviews
This book presents an excellent and thorough introduction and overview of the field. It contains results of 573 papers in the field, but requires few prerequisites beyond basic abstract and linear algebra. It's perfect for independent study.



The key parts of the book for those interested in the matrix multiplication problem, like myself, and related problems are chapters 14-18. Chapter 14 describes the theory of the multiplicative complexity of bilinear maps, of which matrix multiplication is one, in terms of the concept of rank (also tensor rank), especially in the context of matrix algebras. The rank of a bilinear map is essentially a measure of the minimum number of multiplications in a bilinear algorithm for computing the map. Chapter 15 introduces the exponent of matrix multiplication in relation to the asymptotic complexity of the latter, and describes the fundamental relations between these asymptotic and bilinear measures, including the proof of Schonhage's important asymptotic direct sum inequality. Chapter 16 shows the fundamental importance of the exponent because it is found to determine the complexities of other important matrix operations such as inversion, taking of determinants, computing of characteristic polynomials etc. Chapters 17 and 18 describe further extensions, applications and links, including an interesting link between the ranks of finite fields and the minimal distances of linear error-correcting codes.

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Thursday, January 6, 2011

Term Rewriting and All That



Term Rewriting and All That
Franz Baader,Tobias Nipkow | 1998-03-13 00:00:00 | Cambridge University Press | 313 | Theory of Computing
This textbook offers a unified, self-contained introduction to the field of term rewriting. Baader and Nipkow cover all the basic material--abstract reduction systems, termination, confluence, completion, and combination problems--but also some important and closely connected subjects: universal algebra, unification theory, Gröbner bases, and Buchberger's algorithm. They present the main algorithms both informally and as programs in the functional language Standard ML (An appendix contains a quick and easy introduction to ML). Key chapters cover crucial algorithms such as unification and congruence closure in more depth and develop efficient Pascal programs. The book contains many examples and over 170 exercises. This is also an ideal reference book for professional researchers: results spread over many conference and journal articles are collected here in a unified notation, detailed proofs of almost all theorems are provided, and each chapter closes with a guide to the literature.
Reviews
This is a good book for someone researching term rewriting, but it does expect a certain amount of background information. Also, some times the terminology is a little unfamiliar to me (an undergrad math/computer science senior), but a little digging through the index takes care of that problem. All in all, a good book all around, especially if you are used to mathematical writing styles.
Reviews
My main criticism of this book is its title. As a computer science graduate student, I was looking for a somewhat accessible book on the field of term rewriting, and the title of this book made me think it might fulfill my needs. Although the book seems fairly comprehensive, it is very difficult to understand. In fact, I have read several of the papers listed in this book's bibliography and found them more comprehensible. If your math skills are very good, and you prefer equations to english, this may be the book for you.

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Monday, December 27, 2010

The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Popular Science)



The Emperor's New Mind: Concerning Computers, Minds, and the Laws of Physics (Popular Science)
Roger Penrose | 2002-12-12 00:00:00 | Oxford University Press, USA | 640 | Theory of Computing
For decades, proponents of artificial intelligence have argued that computers will soon be doing everything that a human mind can do. Admittedly, computers now play chess at the grandmaster level, but do they understand the game as we do? Can a computer eventually do everything a human mind can do? In this absorbing and frequently contentious book, Roger Penrose--eminent physicist and winner, with Stephen Hawking, of the prestigious Wolf prize--puts forward his view that there are some facets of human thinking that can never be emulated by a machine. Penrose examines what physics and mathematics can tell us about how the mind works, what they can't, and what we need to know to understand the physical processes of consciousness. He is among a growing number of physicists who think Einstein wasn't being stubborn when he said his "little finger" told him that quantum mechanics is incomplete, and he concludes that laws even deeper than quantum mechanics are essential for the operation of a mind. To support this contention, Penrose takes the reader on a dazzling tour that covers such topics as complex numbers, Turing machines, complexity theory, quantum mechanics, formal systems, Godel undecidability, phase spaces, Hilbert spaces, black holes, white holes, Hawking radiation, entropy, quasicrystals, the structure of the brain, and scores of other subjects. The Emperor's New Mind will appeal to anyone with a serious interest in modern physics and its relation to philosophical issues, as well as to physicists, mathematicians, philosophers and those on either side of the AI debate.
Some love it, some hate it, but The Emperor's New Mind, physicist Roger Penrose's 1989 treatise attacking the foundations of strong artificial intelligence, is crucial for anyone interested in the history of thinking about AI and consciousness. Part survey of modern physics, part exploration of the philosophy of mind, the book is not for casual readers--though it's not overly technical, it rarely pauses to let the reader catch a breath. The overview of relativity and quantum theory, written by a master, is priceless and uncontroversial. The exploration of consciousness and AI, though, is generally considered as resting on shakier ground.

Penrose claims that there is an intimate, perhaps unknowable relation between quantum effects and our thinking, and ultimately derives his anti-AI stance from his proposition that some, if not all, of our thinking is non-algorithmic. Of course, these days we believe that there are other avenues to AI than traditional algorithmic programming; while he has been accused of setting up straw robots to knock down, this accusation is unfair. Little was then known about the power of neural networks and behavior-based robotics to simulate (and, some would say, produce) intelligent problem-solving behavior. Whether these tools will lead to strong AI is ultimately a question of belief, not proof, and The Emperor's New Mind offers powerful arguments useful to believer and nonbeliever alike. --Rob Lightner
Reviews
My copy of this book is now 21 years old, but I thought it appropriate to write a short historical review. When I first read this book I was interested to read in a semi-technical way about many of the Physics and Computation ideas of Roger Penrose. I am sure that many are still interested in the book for that reason. Since then Penrose has written other books, but this provides an introduction to his ideas which is half way between popular science and textbook. What has happened in the years that have followed is that this work has undoubtedly stimulated many researchers and others.



The other aspect of the book was his specific arguments about AI: which have ired many critics. Indeed his later book (Shadows of the Mind) contained a revised argument and dealt with about 20 criticisms of the AI argument from this book. Nevertheless this was not enough and more criticisms appeared which he later discussed in other works. So there is quite a trail to follow here for those who wish to take these topics seriously.



I would now suggest that he was really trying to make the case for the importance of non-Turing-Computability in this book. That it is important in scientific arguments from Cognition Theory and AI to Quantum Physics. Non-Turing computability is a very subtle topic to discuss (it was the subject of Turing's logic Ph.D) especially in a philosophically broad way. Many of the topics like Fractals and Penrose Tiling which found their way into this book, and do not immediately seem relevant to the arguments, are there to emphasise and display some non-computable mathematical entities. Oversimplifications of Penrose's arguments usually miss the significance of non-computability in them.



Having said all this I think that were this book to be written now, then some sections could be reworded. As a specific detail I think that in discussing the historical evolution of "algorithm" the definition of that term changes in the book without being noticed. It took me a few readings to notice this.



So if you want to delve into the debate about non-computability in physics and AI this is a book to read, but be aware that it is only the beginning of a longer story. The physics/cosmology discussions are a good introduction to his approach to those topics too.
Reviews
I am just now learning about the quantum aspects of our minds. This pioneer in the study of that subject offers more much than I can understand but still sheds light on his findings.

The University of Arizona's school of Consciousness (Neurology) has a professor teamed up with this author (Dr Hameroff) and together they have expanded these findings into remarkable realms.



We have totally underestimated the capabilities of our minds and certainly the power of Consciousness !

Susanne Zike , Tucson
Reviews
Professor Penrose takes us on a wonderful intellectual voyage as he presents an array of information about consciousness and reality which no one else would put together.



Gradually, he entwines the multicoloured strands to present a polished argument showing why consciousness is non-computational, and no computer, however large, will ever become conscious. While computers may compute better than we can, no computer can understand, as we easily do, why the computation is necessary.



The Emperor's New Mind will have something fascinating for everyone, because of the unexpected things one finds along the road on this thrilling expedition through the classical and quantum universes.




Reviews

I loved this book. I have a basic math & science background, and I am interested in physics but by no means an expert. This book was fascinating and informative and was written in a way to make the knowledge accessible to an educated layman. I cannot recommend it enough.
Reviews
I didn't see it yet, my parents say it's good enough. It was also delivered before estimated date, which is good i guess. We expected a book that is used but in very good condition, and that's what we got. Thanks

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