T Tom Verhoeff

An updated table of minimum-distance bounds for binary linear codes

In 1973 Helgert and Sfinaff published a table of upper and lower bounds on the maximum minimum-distance for binary linear error-correcting codes up to length 127 . This article presents an updated table incorporating numerous improvements that have appeared since then. To simplify the updating task the author has developed a computer program that systematically investigates the consequences of each improvement by applying several well-known general code-construction techniques. This program also made it possible to check the original table. Furthermore, it offers a quick and reliable update service for future improvements.

Delay-insensitive codes : an overview

The problem of delay-insensitive data communication is described. The notion of delay-insensitive code is defined, giving precise conditions under which delay-insensitive data communication is feasible. Examples of these codes are presented and analyzed. It appears that delay-insensitive codes are equivalent with antichains in partially ordered sets and with all unidirectional error-detecting codes.

On computing a longest path in a tree

The primary purpose of this note is to present an exercise in proof design. For us, such a design consists in isolating the relevant concepts for the problem at hand, introducing special-purpose notation for them that is geared to manipulation and to crisp formal specification, and then solving the problem in a demand-driven way, while onthe-fly extracting from the calculation additional theory useful for solving the problem proper. The problem chosen is demonstrating the correctness of an algorithm for computing the longest path in a tree. Given a finite tree with all edges having positive length, we wish to compute a longest path. This can be done using a procedure invented by Edsger W. Dijkstra around 1960, which is as follows. Build a physical model of the tree by connecting each pair of adjacent nodes by a piece of string of the given edge length. Now pick up the physical tree at an arbitrary node U , l t the contraption hang down, and determine a deepest node X. Then pick up the tree at X and determine a deepest node Y . The claim is that the path between X andY is a longest path in the tree. We have never seen a formal proof of this claim, and the purpose of this note is to provide one.

A proposal for an IOI Syllabus

The International Olympiad in Informatics (IOI) is the premier competition in computing science for secondary education. The competition problems are algorithmic in nature, but the IOI Regulations do not clearly define the scope of the competition. The international olympiads in physics, chemistry, and biology do have an official syllabus, whereas the International Mathematical Olympiad has made the deliberate decision not to have an official syllabus. We argue that the benefits of having an official IOI Syllabus outweigh the disadvantages. Guided by a set of general principles we present a proposal for an IOI Syllabus, divided into four main areas: mathematics, computing science, software engineering, and computer literacy.

Transforming Process Algebra Models into UML State Machines: Bridging a Semantic Gap?

There exist many formalisms for modeling the behavior of (software) systems. These formalisms serve different purposes. Process algebras are used for algebraic and axiomatic reasoning about the behavior of distributed systems. UML state machines are suitable for automatic software generation. We have developed a transformation from the process algebra ACP into UML state machines to enable automatic software generation from process algebra models. This transformation needs to preserve both behavioral and structural properties. The combination of these preservation requirements gives rise to a semantic gap. It implies that we cannot transform ACP models into UML state machines on a syntactic level only. We address this semantic gap and propose a way of bridging it. To validate our proposal, we have implemented a tool for automatic transformation of ACP process algebra models into UML state machines.

Networks of Communicating Processes and Their (De-)Composition

In this paper we sketch a general framework within which a study of networks of processes can be conducted. It is based upon the mathematical technique to abstract from irrelevant detail. We start out with a large class of objects and some operations upon them. Depending upon a correctness criterion to be imposed, some of these objects turn out to be equivalent. The resulting space of equivalence classes and operations upon them is, under certain conditions, the (fully) abstract space of interest for that particular correctness concern.

Some new binary, quasi-cyclic codes

By means of local search techniques, five quasi-cyclic codes have been found that have a higher minimum distance than known binary linear codes. The new codes have parameters [102,17,37], [60,20,17], [84,21,27], [105,21,36], and [100,25,30]. Also, 39 other quasi-cyclic codes have been found that improve the parameter sets of previously known quasi-cyclic codes. Twenty-four of them give a new and easier description of binary linear codes with best known parameters.

Analyzing specifications for delay-insensitive circuits

We present the XDI Model for specifying delay-insensitive circuits, that is, reactive systems that correctly exchange signals with their environment in spite of unknown delays incurred by the interface. XDI specifications capture restrictions on the communication between circuit and environment, treating both parties equally. They can be visualized as state graphs where each arrow is labeled by a communication terminal and each state by a safety/progress label. We investigate various properties that can be extracted from XDI specifications: automorphisms, environment partitions, autocomparison matrix, and classifications of choice, order dependence, and nondeterminism. We introduce a distinction between static and dynamic output nondeterminism, capturing the difference between design freedom and arbitration. Determining specification properties is useful for validation and design.

3D turtle geometry: artwork, theory, program equivalence and symmetry

We define a 3D variant of turtle graphics and present the theoretical foundations of 3D turtle geometry. This theory enables one to reason about open and closed 3D polygonal paths by means of algebraic calculations. In particular, we introduce several equivalence relations on turtle programs and theorems that define corresponding standard forms. Also we express the relationship between the symmetries of a 3D polygonal path and the symmetries of a generating turtle program in a suitable standard form. Finally, we discuss software tool support for 3D turtle geometry. Along the way, we present some artworks designed through 3D turtle graphics. These artworks have never been described in the literature before.

Formal design of an asynchronous DSP counterflow pipeline: a case study in handshake algebra

Two recent developments in asynchronous circuit design are explored by means of a case study (polynomial division) in digital signal processing. The first development is a new formal method, the handshake algebra of M.B. Josephs, J.T. Udding and J.T. Yantchev (1993), that is suitable for specifying, deriving, and verifying circuits that follow a handshaking protocol. The second development is an architecture, counterflow pipelines, that R.F. Sproull (1994) has recently suggested, which is attractive to implement asynchronously.