Tool and Object: A History and Philosophy of Category Theory (Science Networks. Historical Studies)

Book Description

Category theory is a general mathematical theory of structures and of structures of structures. It occupied a central position in contemporary mathematics as well as computer science. This book describes the history of category theory whereby illuminating its symbiotic relationship to algebraic topology, homological algebra, algebraic geometry and mathematical logic and elaboratively develops the connections with the epistemological significance.

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Geometric Algebra

Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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Geometric Algebra (Wiley Classics Library)

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ASIN: 0817641998

Book Description

This book presents a unified mathematical treatment of diverse problems in mathematics, physics, computer science and engineering using geometric algebra. This text is a practical resource for professionals, researchers, and practitioners, cyberneticists, computer scientists, engineers, applied physicists and applied mathematicians. Several examples are presented to clarify the importance of geometric algebra in signal and image processing, filtering and neural computer, computer vision, robotics and geometric physics. A useful resource to gain a greater understanding of the potential of geometric algebra for the design and implementation of real time artificial systems.

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I have not read this book, but can provide this information .......2005-01-25

Part I Advances in Geometric Algebra

Chapter 1
Old Wine in New Bottles: A New Algebraic Framework for Computational Geometry,
David Hestenes
1.1 Introduction
1.2 Minkowski Algebra
1.3 Conformal Split
1.4 Models of Euclidean Space
1.5 Lines and Planes
1.6 Spheres and Hyperplanes
1.7 Conformal and Euclidean Groups
1.8 Screw Mechanics
1.9 Conclusions

Chapter 2
Universal Geometric Algebra
Garret Sobczyk
2.1 Introduction
2.2 The Universal Geometric Algebra
2.3 Matrices of Geometric Numbers
2.4 Linear Transformations
2.5 Pseudo-Euclidean Geometries
2.6 Affine and Projective Geometries
2.7 Conformal Transformations

Chapter 3
Realizations of the Conformal Group
Jose Maria Pozo and Garret Sobczyk
3.1 Introduction
3.2 Projective Geometry
3.3 The Conformal Representant and Stereographic Projection
3.4 Conformal Transformations and Isometries
3.5 Isometries in No
3.6 Compactification
3.7 Mobius Transformations

Chapter 4
Hyperbolic Geometry
Hongbo Li
4.1 Introduction
4.2 Hyperbolic Plane Geometry with Clifford Algebra
4.3 Hyperbolic Conformal Geometry with Clifford Algebra
4.4 A Universal Model for the Conformal Geometries of the Euclidean, Spherica and Double-Hyperbolic Spaces
4.5 Conclusion

Part II Theorem Proving

Chapter 5
Geometric Reasoning With Geometric Algebra
Dongming Wang
5.1 Introduction
5.2 Clifford Algebra for Euclidean Geometry
5.4 Proving Identities in Clifford Algebra

Chapter 6
Automated Theorem Proving
Hongbo Li
6.1 Introduction
6.2 A general Framework for Clifford algebra and Wu's Method
6.3 Automated Theorem Proving in Euclidean Geometry and Other
Classical Geometries
6.4 Automated Theorem Proving in Differential Geometry}{116}
6.5 Conclusion

Part III Computer Vision

Chapter 7
The Geometry Algebra of Computer Vision
Eduardo Bayro Corrochano and Joan Lasenby
7.1 Introduction
7.2 The Geometric Algebras of 3-D and 4-D Spaces
7.3 The Algebra of Incidence
7.4 Algebra in Projective Space
7.5 Visual Geometry of $n$ Uncalibrated Camera
7.6 Conclusions

Chapter 8
Using Geometric Algebra for Optical Motion Capture
Joan Lasenby and Adam Stevenson
8.1 Introduction
8.2 External and Internal Calibration
8.3 Estimating the External Parameters
8.4 Examples and Results
8.5 Extending to Include Internal Calibration
8.6 Conclusions

Chapter 9
Bayesian Inference and Geometric Algebra: An Application to Camera Localization
Chris Doran
9.1 Introduction
9.2 Geometric Algebra in Three Dimensions
9.3 Rotors and Rotations
9.4 Rotor Calculus
9.5 Computer Vision
9.6 Unknown range data
9.7 Extension to three cameras
9.8 Conclusions

Chapter 10
Projective Reconstruction of Shape and Motion Using Invariant Theory
Eduardo Bayro Corrochano and Vladimir Banarer
10.1 Introduction
10.2 3-D Projective Invariants from Multiple Views
10.3 Projective Depth
10.4 Shape and Motion
10.5 Conclusions

Part IV Robotics

Chapter 11
Robot Kinematics and Flags

11.1 Introduction
11.2 The Clifford Algebra
11.3 Flags
11.4 Robots
11.5 Concluding Remarks

Chapter 12
The Clifford Algebra and the Optimization of Robot Design
Shawn G. Ahlers and John Michael McCarthy
12.1 Introduction
12.2 Literature Review
12.3 Overview of the Design Algorithm
12.4 Double Quaternions
12.5 The Task Trajectory
12.6 The Design of the TS Robot
12.7 The Optimum TS Robot
12.8 Conclusion

Chapter 13
Eduardo Bayro Corrochano and Garret Sobczyk
13.1 Introduction
13.2 The General Linear Group
13.3 Algebra of Incidence
13.4 Rigid Motion in the Affine Plane
13.5 Application to Robotics
13.6 Application II:
The design of an image filter
Recognition of hand gestures
The meet filter
13.7 Conclusion

Part V Quantum and Neural Computing, and Wavelets

Chapter 14
Geometric Algebra in Quantum Information Processing
by Nuclear Magnetic Resonance
Timothy F. Havel, David G. Cory, Shyamal S. Somaroo, and Ching-Hua Tseng
14.1 Introduction
14.2 Multiparticle Geometric Algebra
14.3 Algorithms for Quantum Computers
14.4 NMR and the Product Operator Formalism
14.5 Quantum Computing by Liquid-State NMR
14.6 States and Gates by NMR
14.7 Quantum Simulation by NMR
14.8 Remarks on Foundational Issues

Chapter 15
Geometric Feedforward Neural Networks and Support Multivector Machines
Eduardo Bayro Corrochano and Refugio Vallejo

15.1 Introduction
15.2 Real Valued Neural Networks
15.3 Complex MLP and Quaternionic MLP
15.4 Geometric Algebra Neural Networks
15.5 Learning Rule
15.6 Experiments Using Geometric Feedforward Neural Networks
15.7 Support Vector Machines in Geometric Algebra
15.8 Experimental Analysis of Support Multivector Machines
15.9 Conclusions

Chapter 16
Image Analysis Using Quaternion Wavelets
Leonardo Traversoni
16.1 Introduction
16.2 The Static Approach
16.3 Clifford Multiresolution Analyses
16.4 Haar Quaternionic Wavelets
16.5 A Dynamic Interpretation
16.6 Global Interpolation
16.7 Dealing with Trajectories
16.8 Conclusions

Part VI Applications to Engineering and Physics

Chapte 17
Objects in Contact: Boundary Collisions as Geometric Wave Propagation
Leo Dorst
17.1 Introduction
17.2 Boundary Geometry
17.3 The Boundary as a Geometric Object
17.4 Wave Propagation of Boundaries
17.5 Conclusions

Chapter 18 Modern Geometric Calculations in Crystallography
G. Aragon, J.L. Aragon, F. Davila, A. Gomez and M.A. Rodriguez
18.1 Introduction
18.2 Quasicrystals
18.3 The Morphology of Icosahedral Quasicrystals
18.4 Coincidence Site Lattice Theory
18.5 Conclusions

Chapter 19 Quaternion Optimization Problems in Engineering
Ljudmila Meister
19.1 Introduction
19.2 Properties of Quaternions
19.3 Extremal Problems for Quaternions
19.4 Determination of Rotations
19.5 The Main Problem of Orientation
19.6 Optimal Filtering and Prediction
19.7 Summary

Chapter 20
Clifford Algebras in Electrical Engineering
William Baylis
20.1 Introduction
20.2 Structure of Cl_3
20.3 Paravector Model of Spacetime
20.4 Using Relativity at Low Speeds
20.5 Relativity at High Speeds
20.6 Conclusions

Chapter 21
Applications of Geometric Algebra in Physics and Links With Engineering
Anthony Lasenby and Joan Lasenby

21.1 Introduction
21.2 The Spacetime Algebra
21.3 Quantum Mechanics
21.4 Gravity as a Gauge Theory
21.5 A New Representation of 6-d Conformal Space
21.6 Summary and Conclusions

Part VII Computational Methods in Clifford Algebras

Chapter 22
Clifford Algebras as Projections of Group Algebras
Vladimir M. Chernov
22.1 Introduction
22.2 Group Algebras and Their Projection
22.3 Applications
22.4 Conclusion

Chapter 23
Counterexamples for Validation and Discovering of New Theorems
Pertti Lounesto
23.1 Introduction
23.2 The Role of Counterexamples in Mathematics
23.3 Clifford Algebras: An Outline
23.4 Preliminary Counterexamples in Clifford Algebras
23.5 Counterexamples About Spin Groups
23.6 Counterexamples on the Internet

Chapter 24
The Making of GABLE: A Geometric Algebra Learning Environment in Matlab
Stephen Mann, Leo Dorst, and Tim Bouma
24.1 Introduction
24.2 Representation of Geometric Algebra
24.3 Inverses
24.4 Meet and Join
24.5 Graphics
24.6 Example: Pappus's Theorem
24.7 Conclusions

Chapter 25
Helmstetter Formula and Rigid Motions with CLIFFORD
Rafal Ablamowicz
25.1 Introduction
25.2 Verification of the Helmstetter Formula
25.3 Rigid Motions with Clifford Algebras
25.4 Summary

References

Index

Algebraic Theory of Automata Networks (SIAM Monographs on Discrete Mathematics and Applications, 11) (Monographs on Discrete Mathematics and Applications)

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Algebraic Theory of Automata Networks (SIAM Monographs on Discrete Mathematics and Applications, 11) (Monographs on Discrete Mathematics and Applications)
Pál Dõmõsi , and Chrystopher L. Nehaniv
Manufacturer: SIAM: Society for Industrial and Applied Mathematics
ProductGroup: Book
Binding: Hardcover

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ASIN: 0898715695

Book Description

Algebraic Theory of Automata Networks investigates automata networks as algebraic structures and develops their theory in line with other algebraic theories. Automata networks are investigated as products of automata, and the fundamental results in regard to automata networks are surveyed and extended, including the main decomposition theorems of Letichevsky, and of Krohn and Rhodes. The text summarizes the most important results of the past four decades regarding automata networks and presents many new results discovered since the last book on this subject was published. Several new methods and special techniques are discussed, including characterization of homomorphically complete classes of automata under the cascade product; products of automata with semi-Letichevsky criterion and without any Letichevsky criteria; automata with control words; primitive products and temporal products; network completeness for digraphs having all loop edges; complete finite automata network graphs with minimal number of edges; and emulation of automata networks by corresponding asynchronous ones.

Principles of Neurocomputing for Science and Engineering

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For beginners and graduate students
For beginners and graduate students

Principles of Neurocomputing for Science and Engineering
Fredric M. Ham , and Ivica Kostanic
Manufacturer: McGraw-Hill Science/Engineering/Math
ProductGroup: Book
Binding: Hardcover

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ASIN: 0070259666

Book Description

* Unlike other neural network books, this is written specifically for scientists and engineers who want to apply neural networks to solve complex problems
* For each neurocomputing concept, a solid mathematical foundation is presented along with illustrative examples to accompany that particular architecture and associated training algorithm
* Incorporates many detailed examples and an extensive set of end-of-chapter problems

Customer Reviews:

For beginners and graduate students.......2001-01-05

I strongly recommend this text for beginners and graduate students who want to understand Neural Networks. First, the text book explains the why, where, and how to apply Neural Networks, which is the most important point for understanding Neural Networks. Second, mathematical proofs, clear description of algorithms and MATLAB codes encourage me to do it myself. And a lot of mathematical foundation in the Appendix allow me to understand quite easily complex mathematical concepts.

For beginners and graduate students.......2001-01-05

History: Fiction or Science? Dating methods as offered by mathematical statistics. Eclipses and zodiacs. Chronology Vol.I

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Calculations are only as good as your numbers
Pants on fire?
Accepted History & Chronology Must Be Changed.
Very Interesting
History as Science Fiction

History: Fiction or Science? Dating methods as offered by mathematical statistics. Eclipses and zodiacs. Chronology Vol.I
Anatoly Fomenko
Manufacturer: Delamere Resources
ProductGroup: Book
Binding: Paperback

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ASIN: 2913621074
Release Date: 2007-03-19

Product Description

History: Fiction or Science? is the most explosive tractate on history ever written - however, every theory it contains, no matter how unorthodox, is backed by solid scientific data. The book is well-illustrated, contains over 446 graphs and illustrations, copies of ancient manuscripts, and countless facts attesting to the falsity of the chronology used nowadays, which never cease to amaze the reader. Eminent mathematician proves that: Jesus Christ was born in 1153 and crucified in 1186 The Old Testament refers to mediaeval events. Apocalypse was written after 1486. Does this sound uncanny? This version of events is substantiated by hard facts and logic - validated by new astronomical research and statistical analysis of ancient sources - to a greater extent than everything you may have read and heard about history before. The dominating historical discourse in its current state was essentially crafted in the XVI century from a rather contradictory jumble of sources such as innumerable copies of ancient Latin and Greek manuscripts whose originals had vanished in the Dark Ages and the allegedly irrefutable proof offered by late mediaeval astronomers, resting upon the power of ecclesial authorities. Nearly all of its components are blatantly untrue! For some of us, it shall possibly be quite disturbing to see the magnificent edifice of classical history to turn into an ominous simulacrum brooding over the snake pit of mediaeval politics. Twice so, in fact: the first seeing the legendary millenarian dust on the ancient marble turn into a mere layer of dirt - one that meticulous unprejudiced research can eventually remove. The second, and greater, attack of unease comes with the awareness of just how many areas of human knowledge still trust the three elephants of the consensual chronology to support them. Nothing can remedy that except for an individual chronological revolution happening in the minds of a large enough number of people.

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Calculations are only as good as your numbers.......2007-08-03

Yes, we can all agree that mainstream history is nearly 100% BS due to politics, economics, ego, problems with dating techniques, and various conspiracies. Agreed. But, I've been researching the distinct possibility that human history (in terms of civilizations) are much more ancient than we've been told, so coming across this book was very interesting to me. I wondered how Fomenko could be wrong (if at all) because he is very persuasive in his presentations. Then it dawned on me. If at previous times in prehistory, due to the various catastrophies that are well documented (comets, asteroids, planetary disruptions, plasma discharge, pole reversals, etc) the Earth was in a different position in relation to the sun, different tilt on its axis, different orbit, different rotation (in terms of velocity and DIRECTION), and the continents were in different positions, then would this not cause the ancients to see the sky (constellations) differently? In other words, is Fomenko making erronious assumptions about the physics of the Earth in pre-history, which then corrupt his data with regards to dating the relevant astrology? The last event to seriously disrupt our planet occured roughly 3500 years ago, according to other good researchers, so is it possible Fomenko has been confused by this? The vastly different physics of our planet in the not so distant past may explain this confusion, which is not to say the "mainstream" version of history is correct; on the contrary. I am not an expert in these fields, but wanted to see if this idea could spark discussion.

Pants on fire?.......2007-07-19

Will people ever read before spamming? Yes, Jesuits could not rewrite world history alone, they had help. Anyway, Dr Prof Acad A.Fomenko does not point to jesuits as the driving force of world wide history manipulation in published volumes 1,2,3;, actually he barely mentions the poor devils. Check it with 'Search inside' feature, please. China is rarely mentioned either, in fact, Dr Fomenko is completely eurocentric. Right, his theory contradicts all mainstream schools of history, because in their actual state they are all built on blatantly erroneus chronology. You don't need a mysterious cabal (conspiracy) to falsify history, the falsification is its modus operandi. It is inherent to history(ians) to falsify (distort) events, as it is inherent to humans to boast as it is inherent to power (authority) to legimize itself by referrring to glorious past made to its own order. Dr Prof Fomenko and team have identified scores of instances of such manipulation in Russian, European, etc.. history, and delivered valid statistical proof thereof. His own 'reconstruction' is completely another story. Forget c14 as a valid method of dating. W.Libby has initially discovered a brilliant method of INDEPENDENT dating. Too bad, c14 method has become a joke after a forced marrige with dendrochronology with consensual chronological scale inbuilt. Radiocarbon method can't stand blind tests, but is so very productive as a rubberstamp.

Accepted History & Chronology Must Be Changed. .......2007-04-09

There is no doubt that history as most know it is a sham, & institution's version of History both University & Church is fradulent & inaccurate. Everything was established with an agenda, The real "Dark Ages" are now when we have access to incredible amounts of information past authorities & more important 'common folk' didn't have but our institutions & educators are slow to evolve because of what has ignorantly & arrogantly been taught for too long. This is on many subjects not just Chronology.

For anyone to question "Why would a Mathematician have anything credible to say of History?" The answer is from Dr. Fomenko's preface in the book: "It would be worthwhile to remind the reader that in the XVI-XVII century Chronology was considered to be a subdivision of Mathematics." These volumes could possibly be some of the most important works to date & should be read by everyone with an interest in History, especially professors & educators who have a duty to the public. I have read both books & must say that 'Chronology 1' has some very eye opening & revolutionary information. Even if these volumes are part true the implications are profound & opens the doors to further investigations & questions which must be done. I speak several different lanquages & must say the logic Dr. Fomenko uses with "inflection" of words & words being read from left to right in one region & right to left in another then written backwards, the removal of vowels & get down to basics of words, or different cities & locations having the same name etc. is correct. Vowel usage has always been optional & varied, actually complicating linquistics & study. The first thing one has to understand is that words never had a fixed spelling in history like we do now, the spelling of words was mutable & regional, as well as names & titles of people were vast, varied & changed, NOTHING WAS FIXED or understood linear. Matters of Life & Death as well as financial profiteering yesterday & today were & are made with ignorant, illogical & conspiratorial views of history & reality, it's time people get closer to the Truth & society collectively grow up.

Very Interesting.......2007-03-07

It is a good proposal and I believe it will mature into something even better in the future. I think it deserves to be read.

History as Science Fiction.......2007-01-10

Anatoly Fomenko has written a very intriguing book, full of pictures, charts, and computer 'proof' of his thesis: backwards of AD900 we don't really know what happened or when. Between AD900 and AD1600 there is more certainty, but there is still a lot of fuzzy ground, and things don't get reliable until we get past the 1600's where the printing press made it very difficult for the perpetrators of this timeline manipulation to change anything that had been committed to print. The Dark Ages did not happen. Books were burned for a reason. One organization has doubled the actual length of its existence by expanding the real chronology. Read why.

I had always wondered why Christ died about AD33 and yet men waited until the 11th century to form the Knights Templar, the Cathars, etc and go after the Holy Land by force. Why the 1000 year gap? Turns out there wasn't more than a 10-12 year gap and he proves it using astronomy. This also implies that the planet is not as old as we have been told, and current Christian and other creationist scientists are already championing that idea without being aware of Fomenko's book. The two groups, creationist scientists and the Russian mathematical analysts corroborate each other. Fascinating.

Of course, all this flies in the face of what we have been told traditionally is the 'proper' chronology of western civilization, and most readers will experience 'cognitive dissonance' in reading this book. It means that our history going backwards from AD1600 becomes progressively more incorrect and unreliable until it cannot be trusted at all... in the space of 700-800 years.

Naturally, the curious, open-minded reader will want to know WHO did this, WHY, and did any of the events we think of as really ancient ever happen?
Dr. Fomenko is a respected scientist/mathematician at Moscow State University who has already answered these questions to the satisfaction of his initially skeptical colleagues. Most of them are now believers, a few still refuse to believe (the usual diehards), and of course the western press has ignored Fomenko's work -- for obvious reasons when you read the book. The ones who perpetrated this chronology ruse have a lot to answer for. They are still with us. That's why this book is a well-kept secret.

I gave the book a 4-star rating because I was unable to check out some of his claims; those I checked were as he said. But if even 1/3 of his claims are true, this punches a big hole in what we think is our history, the meaning of western civilization, our educational process (for repeating the ruse as gospel), and the trustworthiness of the organization that perpetrated this ruse, well-intentioned or not.

This book relates to current research into a Young Earth paradigm, to John Keel's discoveries about our planet, and Fr Malachi Martin's insights (in his now out-of-print books). We are indeed sheep who are manipulated and kept ignorant -- for a reason. While knowing what these men have to say may be the "booby prize" (as in: 'what can you do with this knowledge?'), it will provide interesting reading. Didn't someone say: "...and the Truth will set you free."?? For you to judge if this book contains the truth.

Pristine Transfinite Graphs and Permissive Electrical Networks

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Pristine Transfinite Graphs and Permissive Electrical Networks
Armen H. Zemanian
Manufacturer: Birkhäuser Boston
ProductGroup: Book
Binding: Hardcover

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ASIN: 0817641947

Book Description

A transfinite graph or electrical network of the first rank is obtained conceptually by connecting conventionally infinite graphs and networks together at their infinite extremities. This process can be repeated to obtain a hierarchy of transfiniteness whose ranks increase through the countable ordinals. This idea, which is of recent origin, has enriched the theories of graphs and networks with radically new constructs and research problems. The book provides a more accessible introduction to the subject that, though sacrificing some generality, captures the essential ideas of transfiniteness for graphs and networks. Thus, for example, some results concerning discrete potentials and random walks on transfinite networks can now be presented more concisely. Conversely, the simplifications enable the development of many new results that were previously unavailable. Topics and features: *A simplified exposition provides an introduction to transfiniteness for graphs and networks.*Various results for conventional graphs are extended transfinitely. *Minty's powerful analysis of monotone electrical networks is also extended transfinitely.*Maximum principles for node voltages in linear transfinite networks are established. *A concise treatment of random walks on transfinite networks is developed. *Conventional theory is expanded with radically new constructs. Mathematicians, operations researchers and electrical engineers, in particular, graph theorists, electrical circuit theorists, and probabalists will find an accessible exposition of an advanced subject.

Mathematical Foundation of Geodesy: Selected Papers of Torben Krarup

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Mathematical Foundation of Geodesy: Selected Papers of Torben Krarup

Manufacturer: Springer
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Binding: Hardcover

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ASIN: 3540337652

Book Description

This volume contains selected papers by Torben Krarup, one of the most important geodesists of the 20 ^th century. His writings are mathematically well founded and scientifically relevant. In this impressive collection of papers he demonstrates his rare innovative ability to present significant topics and concepts. Modern students of geodesy can learn a lot from his selection of mathematical tools for solving actual problems.
The collection contains the famous booklet "A Contribution to the Mathematical Foundation of Physical Geodesy" from 1969, the unpublished "Molodenskij letters" from 1973, the final version of "Integrated Geodesy" from 1978, "Foundation of a Theory of Elasticity for Geodetic Networks" from 1974, as well as numerous trend setting papers on the theory of adjustment.

Economics of Information Security (Advances in Information Security)

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Economics of Information Security (Advances in Information Security)

Manufacturer: Springer
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Binding: Hardcover

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Accessories:

ASIN: 1402080891

Book Description

Economics of Information Security applies economics not to generate breakthroughs in theoretical economics, but rather breakthroughs in understanding the problems of security. Security, privacy and trusted computing are examined distinctly, using the tools of economics, and as elements of a larger dynamic system.

Economics of Information Security is designed for researchers and managers struggling to understand the risks in organizations dependent on secure networks. This book is also suitable for students in computer science, policy and management.

Algebraic Informatics: Second International Conference, CAI 2007, Thessalonkik, Greece, May 21-25, 2007, Revised Selected and Invited Papers (Lecture Notes in Computer Science)

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Algebraic Informatics: Second International Conference, CAI 2007, Thessalonkik, Greece, May 21-25, 2007, Revised Selected and Invited Papers (Lecture Notes in Computer Science)

Manufacturer: Springer
ProductGroup: Book
Binding: Paperback

Book Description

This book constitutes the refereed proceedings of the Second International Conference on Algebraic Informatics, CAI 2007, held in Thessaloniki, Greece, in May 2007.

The 10 revised full papers presented together with 9 invited papers were carefully reviewed and selected from 29 submissions. The papers cover topics such as algebraic semantics on graphs and trees, formal power series, syntactic objects, algebraic picture processing, infinite computation, acceptors and transducers for strings, trees, graphs, arrays, etc., and decision problems.

Algebraic Specification of Communication Protocols (Cambridge Tracts in Theoretical Computer Science)

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Algebraic Specification of Communication Protocols (Cambridge Tracts in Theoretical Computer Science)

Manufacturer: Cambridge University Press
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Binding: Hardcover

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ASIN: 0521418836

Book Description

Modern computer networks now circle the world, but the transmission of information among them depends on the many different protocols that define the behavior of the sender and receiver. It is clear therefore, that the accurate description of these protocols is important if harmonious communication is to be maintained. In this book the authors use the formal specification language PSF to provide an unambiguous description of several communication protocols of varying levels of complexity, ranging from the alternating bit protocol to the token ring protocol. Beginners, as well as professionals in the field of communication protocols, will benefit from both the methods of specification described, and the protocols discussed in this book.

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