David Y. Y. Yun

Multi-dimensional systolic networks, for discrete fourier transform

In this paper the problem of computing the Discrete Fourier Transform (DFT) in VLSI is considered. We describe an approach to extend the linear systolic array algorithm to the multidimensional systolic network algorithm. The proposed networks is based on the pipeline design and have regular structure. Among them the mesh-connected network matches, with a small factor, the known theoretical Ω(n<supscrpt>2</supscrpt>) lower bound to the (area × <italic>time</italic><supscrpt>2</supscrpt>) measure of complexity in the planar VLSI.

VLSI designs for redundant binary-coded decimal addition

A binary-coded decimal system provides rapid binary-decimal conversion. However, BCD arithmetic operations are often slow and require complex hardware. One can eliminate the need for carry propagation and thus improve performance of BCD operations by using a redundant binary-coded decimal (RBCD) system. The VLSI design of an RBCD adder is introduced. The design consists of two small PLAs and two four-bit binary adders for one digit of the RBCD adder. The addition delay is constant for n-digit RBCD addition (no carry propagation delay). The VLSI time and space complexities of the design, as well as its layout are presented, showing the regularity of the structures. Two simple algorithms and the corresponding hardware designs for conversion between RBCD and BCD are presented.<<ETX>>

A fast carry-free algorithm and hardware design for extended integer GCD computation

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Binary paradigm and systolic array implementation for residue arithmetic

is well known that finding the greatest common divisor (GCD) of two integers is one of the fundamental computations in exact rational arithmetic, factorization and cryptography. Euclid3 algorithm and its variants are the widely used for GCD computations [Knu 811. However they are not suitable in the parallel computation. Since the whole-word comparisons is required. G.B. Purdy /Pur 831 proposed a different way to compute GCD which requires no comparison. The advantage of the Purdy’s algorithm is provided a possible way to speed up the period of each iteration time by using carry save technique. However, it requires 0( n2) iterations in its worst case where n denotes the number of bits of two inputs. In addition, it requires the additional hardware support to handle the overflow problem. R. P. Brent and H. T. Kung [B&K 85) have developed a plus-minus (PM) algorithm that test only the two least significant bits of two integers. The advantage of the PM algorithm is that the number of the iteration is at most 3.012*n units. In particular, this gives a linear time implementation on a systolic array [B&K 851. Although reaaonabl efficient in its use of silicon area, the delay between first input and first output of a computation for the serial-in-serial-out GCD is great than 3 n time units which may be undesirable long depending on the application. The basic idea in our algorithm is to combine two sequence operations of PM algorithm of BrenbKung into one basic operation, and also to avoid swap operations during the iterations to achieve higher parallelism. It has been proved that for any two n bit integers, the number of iterations of the new algorithm is less than 1.51*n+ 1 time units. A preliminary hardware design shows that the algorithm can be implemented in a simple way which consists of several conventional computer components such ss shift registers, borrow save adder, counter and a small PLA as controller. The algorithm can be extended to find not only the greatest common divisor of two numbers A and B, but also to find a pair of integers (2, y) such that AZ + By =GCD(A,B) with the same time complexity. A scheme to cascade a number of such GCD chips to compute very large GCD’s is also at hand, which alleviates a critical difficulty in such fields as cryptography.

The CMS-HELP expert system

The problem of residue, or modular, arithmetic is fundamental to symbolic and algebraic computation, coding theory and applications, as well as to error-free arithmetic computations. This paper describes novel algorithms that can lead to efficient hardware for arithmetic operations in residue domains. One of the main achievements is in allowing the flexibility of changing moduli. The technology of systolic array has been used to implement one of the most representative operations, the modular multipler. It is shown that a linear systolic array can compute N modular products in time O(N) with constant number of cells.

Software design representation: design object descriptive attribute notation (DODAN)

An expert system known as CMS-HELP has been developed to serve as an on-line consultant to users of the VM/CMS opening system. It assists computer users (novice or experienced), who attempt to use unfamiliar system facilities, by giving prompt advice of a sequence of commands to accomplish a desired user task. The domain for CMS-HELP is the collection of CMS command modules and EXECs at IBM Research. This set of command facilities is treated as data by the expert system. The source of knowledge is mainly provided by the command descriptions and system consultants, who are expert users of these commands. This expert system exemplifies data/knowledge engineering to develop an intelligent agent capable of providing on-line consultation. Thereby, the system serves important functions to both the developers and the users of CMS commands: it makes the programs more usable and understandable and it makes the users more productive and receptive. Thus, the system brings data/knowledge and its users closer together.

A Model-Based Expert System For Digital Systems Design

An approach using frame/constraint for knowledge representation of software design is presented to facilitate software design acquisition and continued usefulness of design information. The representation is independent of the programming language used in software implementation and covers certain basic concepts of software design: control flow, data flow and data abstraction. These basic characteristics of a software design are specified using design object descriptive attribute notation (DODAN) and can be translated into an event-flow diagram based on the Petri-net semantics and a data-dependent diagram based on data-flow semantics. The run-time behavior of the software designed can be interpreted on the basis of the timing constraints. The translation and interpretation are done by sets of production rules. As consumers often change their demands, various dependent flow analyses can help software designers reuse previous designs, figure out the impact of the change, and rectify the design.<<ETX>>

Function Search from Behavioral Description of a Digital System

In this paper, we present a model-based expert system for automatic digital systems design. The goal of digital systems design is to generate a workable and efficient design from high level specifications. The formalization of the design process is a necessity for building an efficient automatic CAD system. Our approach combines model-based, heuristic best-first search, and meta-planning techniques from AI to facilitate the design process. The design process is decomposed into three subprocesses. First, the high-level behavioral specifications are translated into sequences of primitive behavioral operations. Next, primitive operations are grouped to form intermediate-level behavioral functions. Finally, structural function modules are selected to implement these functions. Using model-based reasoning on the primitive behavioral operations level extends the solution space considered in design and provides more opportunity for minimization. Heuristic best-first search and meta-planning tech-niques control the decision-making in the latter two subprocesses to optimize the final design. They also facilitate system maintenance by separating design strategy from design knowledge.

An application of knowledge-base technology in education: a geometry theorem prover

We present a novel approach for automating the functional design of digital systems. Given a set of behavioral specifications, the objective is to produce an optimal functional design which minimizes certain design criteria. One distinct feature of this approach is adding the step of function minimization. That is, the abstraction of the primitive operations into a set of functions that generates the desired behavior attempts to minimize the cost of that set according to the design criteria. For this purpose, it is important to have a powerful search strategy which will lead to a near-optimal solution in a reasonable time. We have adopted best-first search (A (*) algorithm) as the general framework, and developed several domain-specific heuristic functions (h) which control the search process. Preliminary experimental results are reported.

Software requirements specification from a cognitive psychology perspective

1. IntnniuctIon The first time that a student is exposed to formal mathematical proofs normally happens during a high school geometry course. it is well known that this topic causes significant difficulties for both teachers and students. According to [Hoffer 811, geometry is usually rated as the least liked of all subjects. Although proofs are all but welcomed in high school mathematics, it is generally recognized that an understanding of the basic principles underlying mathematical proofs is essential for the development of higher mathematical and logical skiHs.