Infinite Words

Infinite Words is an important theory in both Mathematics and Computer Sciences. Many new developments have been made in the field, encouraged by its application to problems in computer science. Infinite Words is the first manual devoted to this topic. Infinite Words explores all aspects of the theory, including Automata, Semigroups, Topology, Games, Logic, Bi-infinite Words, Infinite Trees and Finite Words. The book also looks at the early pioneering work of Büchi, McNaughton and Schützenberger. Serves as both an introduction to the field and as a reference book. Contains numerous exercises desgined to aid students and readers. Self-contained chapters provide helpful guidance for lectures.

A certain category of infinite strings of letters on a finite alphabet is presented here, chosen among the 'simplest' possible one may build, both because they are very deterministic and because they are built by simple rules (a letter is replaced by a word, a sequence is produced by iteration). These substitutive sequences have a surprisingly rich structure. The authors describe the concepts of quantity of natural interactions, with combinatorics on words, ergodic theory, linear algebra, spectral theory, geometry of tilings, theoretical computer science, diophantine approximation, trancendence, graph theory. This volume fulfils the need for a reference on the basic definitions and theorems, as well as for a state-of-the-art survey of the more difficult and unsolved problems.

A central aim and ever-lasting dream of computer science is to put the development of hardware and software systems on a mathematical basis which is both firm and practical. Such a scientific foundation is needed especially for the construction of reactive programs, like communication protocols or control systems. For the construction and analysis of reactive systems an elegant and powerful theory has been developed based on automata theory, logical systems for the specification of nonterminating behavior, and infinite two-person games. The 19 chapters presented in this multi-author monograph give a consolidated overview of the research results achieved in the theory of automata, logics, and infinite games during the past 10 years. Special emphasis is placed on coherent style, complete coverage of all relevant topics, motivation, examples, justification of constructions, and exercises.

"Not many living artists would be sufficiently brave or inspired to attempt reflecting in art what Borges constructs in words. But the detailed, evocative etchings by Erik Desmazieres provide a perfect counterpoint to the visionary prose. Like Borges, Desmazieres has created his own universe, his own definition of the meaning, topography and geography of the Library of Babel. Printed together, with the etchings reproduced in fine-line duotone, text and art unite to present an artist's book that belongs in the circle of Borges's sacrosanct Crimson Hexagon - "books smaller than natural books, books omnipotent, illustrated, and magical.""--BOOK JACKET.Title Summary field provided by Blackwell North America, Inc. All Rights Reserved

The Beauty of the Infinite is a splendid extended essay in "theological aesthetics." David Bentley Hart here meditates on the power of a Christian understanding of beauty and sublimity to rise above the violence -- both philosophical and literal -- characteristic of the postmodern world. The book begins by tracing the shifting use and nature of metaphysics in the thought of Kant, Hegel, Nietzsche, Heidegger, Lyotard, Derrida, Deleuze, Nancy, Levinas, and others. Hart pays special attention to Nietzsche's famous narrative of the "will to power" -- a narrative largely adopted by the world today -- and he offers an engaging revision (though not rejection) of the genealogy of nihilism, thereby highlighting the significant "interruption" that Christian thought introduced into the history of metaphysics. This discussion sets the stage for a retrieval of the classic Christian account of beauty and sublimity, and of the relation of both to the question of being. Written in the form of a dogmatica minora, this main section of the book offers a pointed reading of the Christian story in four moments, or parts: Trinity, creation, salvation, and eschaton. Through a combination of narrative and argument throughout, Hart ends up demonstrating the power of Christian metaphysics not only to withstand the critiques of modern and postmodern thought but also to move well beyond them. Strikingly original and deeply rewarding, The Beauty of the Infinite is both a constructively critical account of the history of metaphysics and a compelling contribution to it.

This book constitutes the proceedings of the 41st International Conference on Application and Theory of Petri Nets and Concurrency, PETRI NETS 2020, which was supposed to be held in Paris, France, in June 2020. The conference was held virtually due to the COVID-19 pandemic. The 17 regular and 6 tool papers presented together in this volume were carefully reviewed and selected from 56 submissions. The focus of the conference is on following topics: application of concurrency to system design; languages and synthesis; semantics; process mining and applications; extensions and model checking; tools.

The Evolution Arti?cielle cycle of conferences was originally initiated as a forum for the French-speaking evolutionary computation community. Previous EA m- tings were held in Toulouse (EA’94), Brest (EA’95, LNCS 1063), Nˆ?mes (EA’97, LNCS 1363), Dunkerque (EA’99, LNCS 1829), and ?nally, EA 2001 was hosted by the Universit ́e de Bourgogne in the small town of Le Creusot, in an area of France renowned for its excellent wines. However, the EA conferences have been receiving more and more papers from the international community: this conference can be considered fully internat- nal, with 39submissions from non-francophonic countries on all ?ve continents, out of a total of 68. Out of these 68 papers, only 28 were presented orally (41%) due to the formula of the conference (single session with presentations of 30 minutes) that all participants seem to appreciate a lot. The Organizing Committee wishes to thank the members of the International Program Committee for their hard work (mainly due to the large number of submissions) and for the service they rendered to the community by ensuring the high scienti?c content of the papers presented. Actually, the overall quality of the papers presented was very high and all 28 presentations are included in this volume, grouped in 8 sections which more or less re?ect the organization of the oral session: 1. Invited Paper: P. Bentley gave a great talk on his classi?cation of int- disciplinary collaborations, and showed us some of his work with musicians and biologists.