Seven widely held conceptions about formal methods are challenged. These beliefs are variants of the following: formal methods can guarantee that software is perfect; they work by proving that the programs are correct; only highly critical systems benefit from their use; they involve complex mathematics; they increase the cost of development; they are incomprehensible to clients; and nobody uses them for real projects. The arguments are based on the author's experiences. They address the bounds of formal methods, identify the central role of specifications in the development process, and cover education and training. >

Seven myths of formal methods

Determine the value of the variable in each equation.

Basic Algebra = 代数学入門

In this chapter we will present the basic concepts of term rewriting that are needed in this book. More details on term rewriting, its applications, and related subjects can be found in the textbook of Baader and Nipkow [BN98]. Readers versed in German are also referred to the textbooks of Avenhaus [Ave95], Bundgen [Bun98], and Drosten [Dro89]. Moreover, there are several survey articles [HO80, DJ90, Klo92, Pla93] that can also be consulted.

Term Rewriting Systems

Publisher Summary This chapter discusses the mathematical theory of computation. Computation essentially explores how machines can be made to carry out intellectual processes. Any intellectual process that can be carried out mechanically can be performed by a general purpose digital computer. There are three established directions of mathematical research that are relevant to the science of computation—namely, numerical analysis, theory of computability, and theory of finite automata. The chapter explores what practical results can be expected from a suitable mathematical theory. Further, the chapter presents several descriptive formalisms with a few examples of their use and theories that enable to prove the equivalence of computations expressed in these formalisms. A few mathematical results about the properties of the formalisms are also presented.

A Basis for a Mathematical Theory of Computation

. This note addresses the history of process algebra as an area of research in concurrency theory, the theory of parallel and distributed systems in computer science. Origins are traced back to the early seventies of the twentieth century, and developments since that time are sketched. The author gives his personal views on these matters. He also considers the present situation, and states some challenges for the future.

A brief history of process algebra

From the Publisher:
Timing issues are of growing importance for the conceptualization and design of computer-based systems. Timing may simply be essential for the correct behaviour of a system, e.g. of a controller. Even if timing is not essential for the correct behaviour of a system, there may be good reasons to introduce it in such a way that suitable timing becomes relevant for the correct behaviour of a complex system. This book is unique in presenting four algebraic theories about processes, each dealing with timing from a different point of view, in a coherent and systematic way. The timing of actions is either relative or absolute and the underlying time scale is either discrete or continuous. All presented theories are extensions of the algebra of communicating processes. The book is essential reading for researchers and advanced students interested in timing issues in the context of the design and analysis of concurrent and communicating processes.

Process Algebra with Timing

We take a thread as the behavior of a sequential deterministic program under execution and multi-threading as the form of concurrency provided by contemporary programming languages such as Java and C#. We outline an algebraic theory about threads and multi-threading. In the case of multi-threading, some deterministic interleaving strategy determines how threads are interleaved. Interleaving operators for a number of plausible interleaving strategies are specified in a simple and concise way. By that, we show that it is essentially open-ended what counts as an interleaving strategy. We use deadlock freedom as an example to show that there are properties of multi-threaded programs that depend on the interleaving strategy used.

/pdf/thread-algebra-for-strategic-interleaving-1301so0t8n.pdf

Thread algebra for strategic interleaving

This paper gives a comprehensive description of a typed version of the logic known as LPF. This logic is basic to formal specification and verified design in the software development method VDM. If appropriately extended to deal with recursively defined functions, the data types used in VDM, etc., it gives the VDM notation and its associated rules of reasoning. The paper provides an overview of the needed extensions and examines some of them in detail. It is shown how this nonclassical logic-and the extensions-can be reconstructed classically by embeddings into classical infinitary logic.

/pdf/a-typed-logic-of-partial-functions-reconstructed-classically-2po6wv0gyx.pdf

A typed logic of partial functions reconstructed classically

We present an extension of the polarized process algebra BPPA, an algebraic theory about sequential program behaviors. The
extension is called thread algebra and is proposed as a tool for the description and analysis of multi-threaded program behaviors. Strategic interleaving refers to the form of concurrency where some interleaving strategy is used rather than arbitrary interleaving. Strategic interleav-
ing is considered characteristic of multi-threading. Multi-threaded concurrency is more limited than general concurrency based on arbitrary interleaving.

Thread Algebra for Strategic Interleaving

We present real time and discrete time versions of ACP with absolute timing
and relative timing. The startingpoint is a new real time version with absolute
timing, called ACPsat , featuring urgent actions and a delay operator. The discrete time versions are conservative extensions of the discrete time versions of ACP being known as ACPdat and ACPdrt. The principal version is an extension of ACPsat with integration and initial abstraction to allow for choices over an interval of time and relative timing to be expressed. Its main virtue is that it generalizes ACP without timing and most other versions of ACP with timing in a smooth and natural way. This is shown for the real time version with relative timing and the discrete time version with absolute timing.

Cornelis A. Middelburg

Papers

Process Algebra with Timing

Thread algebra for strategic interleaving

A typed logic of partial functions reconstructed classically

Thread Algebra for Strategic Interleaving

Process algebra with timing: Real time and discrete time