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E-grāmata: Collected Works of J. Richard Buchi

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  • Formāts: PDF+DRM
  • Izdošanas datums: 06-Dec-2012
  • Izdevniecība: Springer-Verlag New York Inc.
  • Valoda: eng
  • ISBN-13: 9781461389286
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Collected Works of J. Richard BuchiPalielināt
  • Formāts: PDF+DRM
  • Izdošanas datums: 06-Dec-2012
  • Izdevniecība: Springer-Verlag New York Inc.
  • Valoda: eng
  • ISBN-13: 9781461389286
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Buchi (1924-1984) is known for his work in mathematical logic and theoretical computer science. His papers (some in German) are grouped by subject area, and accompanied by requested comments introducing and evaluating his work in each area. Introductory material discusses Buchi's life and work in general terms. The writings as published here are reproduced from previous publications or manuscripts; the quality and clarity of the typefaces are variable. Annotation copyright Book News, Inc. Portland, Or.

J. Richard Biichi is well known for his work in mathematical logic and theoretical computer science. (He himself would have sharply objected to the qualifier "theoretical," because he more or less identified science and theory, using "theory" in a broader sense and "science" in a narrower sense than usual.) We are happy to present here this collection of his papers. I (DS)1 worked with Biichi for many years, on and off, ever since I did my Ph.D. thesis on his Sequential Calculus. His way was to travel locally, not globally: When we met we would try some specific problem, but rarely dis­ cussed research we had done or might do. After he died in April 1984 I sifted through the manuscripts and notes left behind and was dumbfounded to see what areas he had been in. Essentially I knew about his work in finite au­ tomata, monadic second-order theories, and computability. But here were at least four layers on his writing desk, and evidently he had been working on them all in parallel. I am sure that many people who knew Biichi would tell an analogous story.
1. The Person and His Work.- J. Richard Büchi (19241984).- The Life of
J. Richard Büchi.- The Work of J. Richard Büchi.- The Role of Büchis
Automata in Computer Science.- J. Richard Büchis Doctoral Students.-
Abstracts Published by J. Richard Büchi.-
2. The Publications, with
Comments.- Section
1. Boolean Algebras.- [ 1] Die Boolesche Partialordnung
und die Paarung von Gefügen.- [ 2] Representation of Complete Lattices by
Sets.- [ 3] Investigation of the Equivalence of the Axiom of Choice and Zorns
Lemma from the Viewpoint of the Hierarchy of Types.- Section
2. Discrete
Spaces.- [ 4] On the Existence of Totally Heterogeneous Spaces.- [ 19] Jordan
Circuits of a Graph (with Gary Haggard).- [ 37] Skolem Rings and Their
Varieties (with T. Michael Owens).- Section
3. Towards a Theory of
Definability.- [ 5] The Theory of Proportionality as an Abstraction of Group
Theory (with Jesse B. Wright).- [ 6] Invariants of the Anti-Automorphisms of a
Group (with Jesse B. Wright).- [ 21] Model Theoretic Approaches to
Definability.- [ 22] Definability in Normal Theories (with Kenneth J.
Danhof).- [ 23] Variations on a Theme of Cantor in the Theory of Relational
Structures.- [ 40] Relatively Categorical and Normal Theories.- Abstract
11.
Relatively Categorical and Normal Theories.- Section
4. Automata and
Grammars.- [ 10] Mathematische Theorie des Verhaltens endlicher Automaten.-
Mathematical Theory of the Behavior of Finite Automata (English translation
by Sylvia Büchi, Peter Deussen, and Dirk Siefkes).- [ 11] Regular Canonical
Systems.- [ 12] Algebraic Theory of Feedback in Discrete Systems.- [ 17]
Canonical Systems which Produce Periodic Sets (with William H. Hosken).-
Section
5. Automata and Monadic Theories.- [ 7] Weak Second-Order Arithmetic
and Finite Automata.- [ 8] On aDecision Method in Restricted Second Order
Arithmetic.- [ 13] Transfinite Automata Recursions and Weak Second Order
Theory of Ordinals.- [ 14] Decision Methods in the Theory of Ordinals.- [ 16]
Definability in the Monadic Second-Order Theory of Successor (with Lawrence
H. Landweber).- [ 26] The Complete Extensions of the Monadic Second Order
Theory of Countable Ordinals (with Dirk Siefkes).- [ 28] Deterministic
Automata and the Monadic Theory of Ordinals
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