This monograph contains the results of our joint research over the last ten years on the logic of the fixed point operation. The intended au dience consists of graduate students and research scientists interested in mathematical treatments of semantics. We assume the reader has a good mathematical background, although we provide some prelimi nary facts in Chapter 1. Written both for graduate students and research scientists in theoret ical computer science and mathematics, the book provides a detailed investigation of the properties of the fixed point or iteration operation. Iteration plays a fundamental role in the theory of computation: for example, in the theory of automata, in formal language theory, in the study of formal power series, in the semantics of flowchart algorithms and programming languages, and in circular data type definitions. It is shown that in all structures that have been used as semantical models, the equational properties of the fixed point operation are cap tured by the axioms describing iteration theories. These structures include ordered algebras, partial functions, relations, finitary and in finitary regular languages, trees, synchronization trees, 2-categories, and others.

The semantics of concurrent systems is one of the most vigorous areas of research in theoretical computer science, but suffers from disagree ment due to different, and often incompatible, attitudes towards abstracting non-sequential behaviour. When confronted with process algebras, which give rise to very elegant, highly abstract and com positional models, traditionally based on the interleaving abstraction, some argue that the wealth of contribution they have made is partially offset by the difficulty in dealing with topics such as faimess. On the other hand, the non-interleaving approaches, based on causality, although easing problems with fairness and confusion, still lack struc ture, compositionality, and the elegance of the interleaving counter parts. Since both these approaches have undoubtedly provided important contributions towards understanding of concurrent systems, one should concentrate on what they have in common, rather than the way they differ. The Intemational Workshop on Semantics for Concurrency held at the University of Leicester on 23-25 July 1990 was organised to help overcome this problem. Its main objective was not to be divisive, but rather to encourage discussions leading towards the identification of the positive objective features of the main approaches, in the hope of furthering common understanding. The Workshop met with an excel lent response, and attracted contributions from all over the world. The result was an interesting and varied programme, which was a combi nation of invited and refereed papers. The invited speakers were: Prof. dr. E. Best (Hildesheim University) Prof. dr. A.

From the reviews: "..., the book must be of great help for a researcher who already has some idea of Lie theory, wants to employ it in his everyday research and/or teaching, and needs a source for customary reference on the subject. From my viewpoint, the volume is perfectly fit to serve as such a source, ... On the whole, it is quite a pleasure, after making yourself comfortable in that favourite office armchair of yours, just to keep the volume gently in your hands and browse it slowly and thoughtfully; and after all, what more on Earth can one expect of any book?" --The New Zealand Mathematical Society Newsletter

This book constitutes the refereed proceedings of the 6th International Conference on Algebraic Methodology and Software Engineering, AMAST'97, held in Sydney, Australia, in December 1997. The volume presents 48 revised full papers selected from an unusually high number of submissions. One of the outstanding features of AMAST is its mix of serious mathematical development of formal methods in software engineering with practical concerns, tools, case studies, and industrial development. The volume addresses all current aspects of formal methods in software engineering and programming methodology, with a certain emphasis on algebraic and logical foundations.

Annotation This book constitutes the refereed proceedings of the Third International Conference on Algebraic Informatics, CAI 2009, held in Thessaloniki, Greece, in May 2009. The 16 full papers were carefully reviewed and selected from 25 submissions. The papers cover topics such as algebraic semantics on graph and trees, formal power series, syntactic objects, algebraic picture processing, finite and infinite computations, acceptors and transducers for strings, trees, graphs arrays, etc. decision problems, algebraic characterization of logical theories, process algebra, algebraic algorithms, algebraic coding theory, algebraic aspects of cryptography.

This book gives an introduction to index theory for symplectic matrix paths and its iteration theory, as well as applications to periodic solution problems of nonlinear Hamiltonian systems. The applications of these concepts yield new approaches to some outstanding problems. Particular attention is given to the minimal period solution problem of Hamiltonian systems and the existence of infinitely many periodic points of the Poincaré map of Lagrangian systems on tori.