Bernhard Möller - Böcker

The book serves as a systematic exposition of modal semirings. Next to motivating the definitions, developing the basic calculus and discussing the most interesting examples of modal semirings, it presents a wide variety of applications. On the side of program semantics, Hoare Logic, the theory of general and partial correctness, demonic semantics and various temporal logics such as PDL, LTL andCTL* are treated. The book is situated in the general area of formal methods. Among the many approaches there, it concentrates on a strongly calculational style using algebra as its main ingredient. This field is often called \emph{algebraic logic}. Its aim is to compact series of small steps of general logical inference into larger (in)equational steps. Moreover, it attempts to replace tedious model-theoretic argumentation, in particular, element-wise argumentation, by more abstract and compact reasoning. The structure of the book is as follows: Part I presents the basic theory. Part II contains applications to program semantics, graph-theoretic algorithms, Epistemic Logic, game analysis and databases with preference relations. Part III deals with infinite computations as well as their application to the above-mentioned temporal logics and Neighbourhood Logic as used in the description of hybrid systems. Part IV presents further applications to program semantics and terminations analysis.Finally, Part V contains some advanced theoretical material.Whereas Part I should be read sequentially, the chapters in the other parts are more or less independent of each other.​

This volume contains the proceedings of the 7th International Seminar on - lational Methods in Computer Science (RelMiCS 7) and the 2nd International Workshop onApplications ofKleeneAlgebra.Thecommonmeetingtookplacein Bad Malente (near Kiel), Germany,from May May 12-17,2003.Its purpose was to bring together researchers from various subdisciplines of Computer Science, Mathematics and related ?elds who use the calculi of relations and/or Kleene algebra as methodological and conceptual tools in their work. This meeting is the joint continuation of two di?erent series of meetings. Previous RelMiCS seminars were held in Schloss Dagstuhl (Germany) in J- uary 1994, Parati (Brazil) in July 1995, Hammamet (Tunisia) in January 1997, Warsaw (Poland) in September 1998, Quebec (Canada) in January 2000, and Oisterwijk (The Netherlands) in October 2001. The ?rst workshop on appli- tions of Kleene algebra was also held in Schloss Dagstuhl in February 2001. To join these two events in a common meeting was mainly motivated by the s- stantialcommoninterestsandoverlapofthetwocommunities.Wehopethatthis leads to fruitful interactions and opens new and interesting research directions.

ThisvolumecontainstheproceedingsofMPC2002,thesixthinternationalc- ferenceontheMathematicsofProgramConstruction.Thisseriesofconferences aims to promote the development of mathematical principles and techniques that are demonstrably useful and usable in the process of constructing c- puter programs (whether implemented in hardware or software). The focus is ontechniquesthatcombineprecisionwith conciseness,enablingprogramsto be constructed by formal calculation. Within this theme, the scope of the series is verydiverse,including programmingmethodology,programspeci?cationand transformation, programming paradigms, programming calculi, and progr- ming language semantics. The quality of the papers submitted to the conference was in general very high, and the number of submissions was comparable to that for the previous conference.Eachpaperwasrefereedbyatleastfour,andoftenmore,committee members.Inadditiontothe11papersselectedforpresentationbytheprogramcomm- tee, this volume contains three invited talks: Implementing Algebraic Dynamic Programming in the Functional and the Imperative Programming Paradigm by Robert Giegerich (Technical University of Bielefeld, Germany), and abstracts of Some Results in Dynamic Model Theory by Dexter Kozen (Cornell Univ- sity,USA)and Mathematics in Computer Science Curricula byJeannetteWing (Carnegie Mellon University, USA). The conference took place in Dagstuhl, Germany. The previous ?ve conf- ences wereheld in 1989in Twente,The Netherlands, in 1992in Oxford,United Kingdom,in1995inKlosterIrsee,Germany,in1998inMarstrandnearGot .. eborg in Sweden, and in 2000 in Ponte de Lima, Portugal. The proceedings of these conferenceswerepublishedasLNCS375,669,947,1422,and1837,respectively. Three international events were co-located with the conference: the IFIP WG2.1 working conference on Generic Programming, the third workshop on Constructive Methods for Parallel Programming, and the workshop on Types in Programming. We thank the organizers of these events for their interest in sharing the atmosphere of the conference.

This volume contains the background texts for an IFIPState-of-the-Art Seminar on Formal Program Development, heldin early 1992 near Rio de Janeiro, Brazil. The book stems from work done by IFIP Working Group 2. 1 onAlgorithmic Languages and Calculi. Since 1975, the WorkingGroup has increasingly focused on systematic approaches toprogramming and on appropriate concepts and notations tosupport such approaches. Today, the calculation of programsfrom specifications constitutes the central theme ofthegroup's work. Thus the core interests of the group are:- formal specification of solutions to problems, and- formal development/calculationof programs from suchspecifications.

This volume contains the final revised versions of the best papers presented at the First International Workshop on Higher-Order Algebra, Logic, and Term Rewriting (HOA '93), held in Amsterdam in September 1993. Higher-Order methods are increasingly applied in functional and logic programming languages, as well as in specification and verification of programs and hardware. The 15 full papers in this volume are devoted to the algebra and model theory of higher-order languages, computational logic techniques including resolution and term rewriting, and specification and verification case studies; in total they provide a competently written overview of current research and suggest new research directions in this vigourous area.

This volume constitutes the proceedings of the Third International Conference on the Mathematics of Program Construction, held at Kloster Irsee, Germany in July 1995.Besides five invited lectures by distinguished researchers there are presented 19 full revised papers selected from a total of 58 submissions. The general theme is the use of crisp, clear mathematics in the discovery and design of algorithms and in the development of corresponding software and hardware; among the topics addressed are program transformation, program analysis, program verification, as well as convincing case studies.

This book presents a collection of revised refereed papers selected from the presentations accepted for the Second International Workshop on Higher-Order Algebra, Logic, and Term Rewriting, HOA '95, held in Paderborn, Germany, in September 1995.The 14 research papers included, together with an invited paper by Jan Willem Klop, report state-of-the-art results; the relevant theoretical aspects are addressed, and in addition existing proof systems and term rewriting systems are discussed.

This volume is devoted to the theoretical foundations of hardware design. The 12 chapters presented are organized in sections on mathematical foundations of hardware modelling; models of hardware and dynamical systems; and verification and deductive design of systems. The book is a memoir documenting scientific work done by the NADA Working Group within ESPRIT Basic Research Action 8533.The chapters address theoretical topics including stream processing, spatially extended systems, hierarchical structures, and integration of digital analogue models. There are case studies of superscalar processors, the Java Virtual Machine, and biological excitable media; various design and verification techniques are presented.

This volume contains the proceedings of the 10th International Seminar on - lational Methods in Computer Science (RelMiCS 10) and the 5th International Workshop on Applications of Kleene Algebra (AKA 5). The joint conference took place in Frauenwo ..rthon an Island in Lake Chiem in Bavaria,April 7-April 11, 2008. Its purpose was to bring together researchers various subdisciplines of computer science, mathematics and related ?elds who use the calculus of - lations and/or Kleene algebra as methodological and conceptual tools in their work. This conference is the joint continuation of two di?erent strands of meetings. The seminars of the RelMiCS series were held in Schloss Dagstuhl (Germany) in January 1994, Parati (Brazil) in July 1995, Hammamet (Tunisia) in January 1997, Warsaw (Poland) in September 1998, Qu' ebec (Canada) in January 2000, and Oisterwijk (The Netherlands) in October 2001. The meeting on Appli- tions of Kleene Algebra started as a workshop, also held in Schloss Dagstuhl, in February2001.Tojointhesetwothemesinoneconferencewasmainlymotivated by the substantial common interests and overlap of the two communities.Over the years this has led to fruitful interactions and openened new and interesting researchdirections.Jointmeetings havebeenheldinMalente(Germany)in May 2003, in St. Catherines (Canada) in February 2005 and in Manchester (UK) in August/September 2006. This volume contains 28 contributions by researchersfrom all overthe world.

The book constitutes the joint refereed proceedings of the 11th International Conference on Relational Methods in Computer Science, RelMiCS 2009, and the 6th International Conference on Applications of Kleene Algebras, AKA 2009, held in Doha, Qatar in November 2009. The 22 revised full papers presented together with 2 invited papers were carefully reviewed and selected from numerous submissions. The papers describe the calculus of relations and similar algebraic formalisms as methodological and conceptual tools with special focus on formal methods for software engineering, logics of programs and links to neighbouring disciplines. Their scope comprises relation relation algebras and Kleene algebras, related formalisms such as process algebras, fixed point calculi, idempotent semirings, quantales, allegories, dynamic algebras, cylindric algebras and their applications in areas such as verification, analysis and development of programs and algorithms relational formal methods such as B or Z, tabular methods, algebraic approaches to logics of programs, modal and dynamic logics, interval and temporal logics, algebraic semantics of programming languages , graph theory and combinatorial optimization, games, automata and language theory, mechanised and automated reasoning, decision procedures, spatio-temporal reasoning, knowledge acquisition, preference and scaling methods or information systems.