The Idea of Program Refinement Programs are complex. They are typically so complex, that they go beyond the full comprehension even of the programmer or team who designed them, with all the consequences this has. How can we cope with such complexity in a satisfactory way? An approach, advocated for a long time, is to separate a concise specification of a program - the "what" - from a possibly involved implementation - the "how". Once a specification is obtained from the set of requirements on the program, there can still be a large gap to an efficient implementation. The development from specification to implementation can then proceed by a succession oflayers, such that each layer is a refinement of the previous one. Design decisions can be introduced in refinement steps one at a time. By this, the refinement steps can be kept small and manageable.

Natural Language Processing is the branch of Artificial Intelligence involving language, be it in spoken or written modality. Teaching Natural Language Processing (NLP) is difficult because of its inherent connections with other disciplines, such as Linguistics, Cognitive Science, Knowledge Representation, Machine Learning, Data Science, and its latest avatar: Deep Learning. Most introductory NLP books favor one of these disciplines at the expense of others.

From the viewpoint of an "industrial" this book is most welcome, as one of the most significant demonstrations of the maturity of Prolog. Logic programming is a fascinating area in computer science, which held for years - and still does - the promise of freeing ourselves from programming based on the "Von Neumann" machine. In addition computer programming has long been for solid theoretical foundations. While conventional engineering, dealing mainly with "analogical complexity", developed over some hundred years a complete body of mathematical tools, no such toolset was available for "digital complexity". The only mathematical discipline which deals with digital complexity is logic and Prolog is certainly the operational tool which comes closest to the logical programming ideal. So, why does Prolog, despite nearly twenty years of development, still appear to many today to be more of a research or academic tool, rather than an industrial programming language? A few reasons may explain this: First, I think Prolog suffers from having been largely assimilated into - and thus followed the fate of - Artificial Intelligence. Much hype in the late 1980 created overexpectations and failed to deliver, and the counterreaction threw both AI and Prolog into relative obscurity. In a way, maybe this is a new chance for the Prolog community: the ability to carry out real work and progress without the disturbance of limelights and the unrealistic claims of various gurus. Second, programming in Prolog is a new experience for computer professionals.

The finite - infinite interplay is central in human thinking, from ancient philosophers and mathematicians (Zeno, Pythagoras), to modern mathe­ matics (Cantor, Hilbert) and computer science (Turing, Godel). Recent developments in mathematics and computer science suggest a) radically new answers to classical questions (e. g. , does infinity exist?, where does infinity come from?, how to reconcile the finiteness of the human brain with the infinity of ideas it produces?), b) new questions of debate (e. g. , what is the role played by randomness?, are computers capable of handling the infinity through unconventional media of computation?, how can one approximate efficiently the finite by the infinite and, conversely, the infinite by finite?). Distinguished authors from around the world, many of them architects of the mathematics and computer science for the new century, contribute to the volume. Papers are as varied as Professor Marcus' activity, to whom this volume is dedicated. They range from real analysis to DNA com­ puting, from linguistics to logic, from combinatorics on words to symbolic dynamics, from automata theory to geography, and so on, plus an incursion into the old history of conceptions about infinity and a list of philosophical "open problems". They are mainly mathematical and theoretical computer science texts, but not all of them are purely mathematical.

This book constitutes the refereed proceedings of the 30th International Symposium on Static Analysis, SAS 2023, held in Lisbon, Portugal, in October 2023. The 20 full papers included in this book were carefully reviewed and selected from 40 submissions. Static analysis is widely recognized as a fundamental tool for program verification, bug detection, compiler optimization, program understanding, and software maintenance. The papers deal with theoretical, practical and application advances in the area.

Information is an important concept that is studied extensively across a range of disciplines, from the physical sciences to genetics to psychology to epistemology. Information continues to increase in importance, and the present age has been referred to as the “Information Age.”

This book discusses the use of the real numbers in theorem proving. Typ­ ically, theorem provers only support a few 'discrete' datatypes such as the natural numbers. However the availability of the real numbers opens up many interesting and important application areas, such as the verification of float­ ing point hardware and hybrid systems. It also allows the formalization of many more branches of classical mathematics, which is particularly relevant for attempts to inject more rigour into computer algebra systems. Our work is conducted in a version of the HOL theorem prover. We de­ scribe the rigorous definitional construction of the real numbers, using a new version of Cantor's method, and the formalization of a significant portion of real analysis. We also describe an advanced derived decision procedure for the 'Tarski subset' of real algebra as well as some more modest but practically useful tools for automating explicit calculations and routine linear arithmetic reasoning.

This book contains the refereed proceedings of the 20th International Conference on Theorem Proving in Higher Order Logics, TPHOLs 2007, held in Kaiserslautern, Germany, September 2007. Among the topics of this volume are formal semantics of specification, modeling, and programming languages, specification and verification of hardware and software, formalization of mathematical theories, advances in theorem prover technology, as well as industrial application of theorem provers.

Formal Languages and Applications provides a comprehensive study-aid and self-tutorial for graduates students and researchers.

This Festschrift volume is published in memory of William W. McCune who passed away in 2011. William W. McCune was an accomplished computer scientist all around but especially a fantastic system builder and software engineer.
The volume includes 13 full papers, which are presenting research in all aspects of automated reasoning and its applications to mathematics. These papers have been thoroughly reviewed and selected out of 15 submissions received in response to the call for paper issued in September 2011. The topics covered are: strategies, indexing, superposition-based theorem proving, model building, application of automated reasoning to mathematics, as well as to program verification, data mining, and computer formalized mathematics.

Over time, basic research tends to lead to specialization – increasingly narrow t- ics are addressed by increasingly focussed communities, publishing in increasingly con ned workshops and conferences, discussing increasingly incremental contri- tions. Already the community of programming languages is split into various s- communities addressing different aspects and paradigms (functional, imperative, relational, and object-oriented). Only a few people manage to maintain a broader view, and even fewer step back in order to gain an understanding about the basic principles, their interrelation, and their impact in a larger context.

Fundamental Problems in Computing is in honor of Professor Daniel J. Rosenkrantz, a distinguished researcher in Computer Science. Professor Rosenkrantz has made seminal contributions to many subareas of Computer Science including formal languages and compilers, automata theory, algorithms, database systems, very large scale integrated systems, fault-tolerant computing and discrete dynamical systems. For many years, Professor Rosenkrantz served as the Editor-in-Chief of the Journal of the Association for Computing Machinery (JACM), a very prestigious archival journal in Computer Science. His contributions to Computer Science have earned him many awards including the Fellowship from ACM and the ACM SIGMOD Contributions Award.

Challenges arise when the size of a group of cooperating agents is scaled to hundreds or thousands of members. In domains such as space exploration, military and disaster response, groups of this size (or larger) are required to achieve extremely complex, distributed goals. To effectively and efficiently achieve their goals, members of a group need to cohesively follow a joint course of action while remaining flexible to unforeseen developments in the environment.

"I prefer to view formal methods as tools. the use of which might be helpful." E. W. Dijkstra Algebraic specifications are about to be accepted by industry. Many projects in which algebraic specifications have been used as a design tool have been carried out. What prevents algebraic specifications from breaking through is the absence of introductory descriptions and tools supporting the construction of algebraic specifications. On the one hand. interest from industry will stimulate people to make introductions and tools. whereas on the other hand the existence of introductions and tools will stimulate industry to use algebraic specifications.