From the Publisher:
Your book fills the gap which all of us felt existed too long. Congratulations on this excellent contribution to our field."
--Jan van Leeuwen, Utrecht University 

"This is an impressive book. The subject has been thoroughly researched and carefully presented. All the machine models central to the modern theory of computation are covered in depth; many for the first time in textbook form. Readers will learn a great deal from the wealth of interesting material presented."
--Andrew C. Yao, Professor of Computer Science, Princeton University

"Models of Computation" is an excellent new book that thoroughly covers the theory of computation including significant recent material and presents it all with insightful new approaches. This long-awaited book will serve as a milestone for the theory community."
--Akira Maruoka, Professor of Information Sciences, Tohoku University

"This is computer science."
--Elliot Winard, Student, Brown University

In Models of Computation: Exploring the Power of Computing, John Savage re-examines theoretical computer science, offering a fresh approach that gives priority to resource tradeoffs and complexity classifications over the structure of machines and their relationships to languages. This viewpoint reflects a pedagogy motivated by the growing importance of computational models that are more realistic than the abstract ones studied in the 1950s, '60s and early '70s. 

Assuming onlysome background in computer organization, Models of Computation uses circuits to simulate machines with memory, thereby making possible an early discussion of P-complete and NP-complete problems. Circuits are also used to demonstrate that tradeoffs between parameters of computation, such as space and time, regulate all computations by machines with memory. Full coverage of formal languages and automata is included along with a substantive treatment of computability. Topics such as space-time tradeoffs, memory hierarchies, parallel computation, and circuit complexity, are integrated throughout the text with an emphasis on finite problems and concrete computational models 
FEATURES:
Includes introductory material for a first course on theoretical computer science. Builds on computer organization to provide an early introduction to P-complete and NP-complete problems. Includes a concise, modern presentation of regular, context-free and phrase-structure grammars, parsing, finite automata, pushdown automata, and computability. Includes an extensive, modern coverage of complexity classes. Provides an introduction to the advanced topics of space-time tradeoffs, memory hierarchies, parallel computation, the VLSI model, and circuit complexity, with parallelism integrated throughout. Contains over 200 figures and over 400 exercises along with an extensive bibliography. 

** Instructor's materials are available from your sales rep. If you do not know your local sales representative, please call 1-800-552-2499 for assistance, or use the Addison Wesley Longman rep-locator at ...

Models of Computation: Exploring the Power of Computing

Image processing problems frequently involve large structured arrays of data and a need for very rapid computation. Special parallel processing schemes have evolved over the last 20 years to deal with these problems. In this paper many parallel systems which have been developed for image processing are outlined and the features of their underlying architectures are discussed. Most of these special architectures may be loosely classified as either SIMD or pipeline structures although some MIMD structures have been designed for high level image analysis. In recent years several multiple SIMD (MSIMD) schemes have been proposed as suitable architectures for image processing. The fundamental problems of developing an effective MSIMD system are discussed and a simple SIMD/MIMD computational model for comparison with such systems is proposed.

Parallel computer architectures for image processing

In this correspondence, a parallel 2-D convolution scheme is presented. The processing structure is a mesh connected array processor consisting of the same number of simple processing elements as the number of pixels in the image. For most windows considered, the number of computation steps required is the same as that of the coefficients of a convolution window. The proposed scheme can be easily extended to convolution windows of arbitrary size and shape. The basic idea of the proposed scheme is to apply the 1-D systolic concept to 2-D convolution on a mesh structure. The computation is carried out along a path called a convolution path in a systolic manner. The efficiency of the scheme is analyzed for windows of various shapes. The ideal convolution path is a Hamiltonian path ending at the center of the window, the length of which is equal to the number of window coefficients. The simple architecture and control strategy make the proposed scheme suitable for VLSI implementation.

Parallel 2-D Convolution on a Mesh Connected Array Processor

Pipelining computations over a large array of cells has been an important feature of systolic arrays. To achieve even higher degrees of concurrency, it is desirable to have cells of a systolic array themselves be pipelined as well. The resulting two-level pipelined systolic array would enjoy in principle a k-fold increase in its throughput, where k is the ratio of the time to perform the entire cell computation over that to perform just one of its pipeline stages. This paper describes such a two-level pipelined systolic array that is capable of performing convolutions of any dimension. The designs take full advantages of the pipelining assumed to be available at each cell.

A Two-Level Pipelined Systolic Array for Convolutions

Median smoothing, a filtering technique with wide application in digital signal and image processing, involves replacing each sample in a grid with the median of the samples within some local neighborhood. As implemented on conventional computers, this operation is extremely expensive in both computation and communication resources. This paper defines the running order statistics (ROS) problem, a generalization of median smoothing. It then summarizes some of the issues involved in the design of special purpose devices implemented with very large scale integration (VLSI) technology. Finally, it presents algorithms designed for VLSI implementation which solve the ROS problem and are efficient with respect to hardware resources, computation time, and communication bandwidth.

Systolic Algorithms for Running Order Statistics in Signal and Image Processing

: This paper describes a chip for performing the 2-D (two-dimensional) convolution in signal and image processing. The chip, based on a systolic design, consists of essentially only one type of simple cells, which are mesh-interconnected in a regular and modular way, and achieves high performance through extensive concurrent and pipelined use of these cells. Denoting by u the cycle time of the basic cell, the chip allows convolving a kxk window with an nxn image in O(sq m)(u/k) time, using a total of cu k basic cells. The total number of cells is optimal in the sense that the usual sequential algorithm takes O(sq m)(sq k)(u) time. Furthermore, because of the modularity of the design, the number of cells used by the chip can be easily adjusted to achieve any desirable balance between I/O and computation speeds. (Author)

/pdf/a-systolic-2-d-convolution-chip-4u9lvq741i.pdf

H T Kung

Papers

A systolic 2-D convolution chip