The Work of J. Richard Büchi

  • Dirk Siefkes


J. Richard Büchi has done influential work in mathematics, logic, and computer sciences. He is probably best known for using finite automata as combinatorial devices to obtain strong results on decidability and definability in monadic second order theories, and extending the method to infinite combinatorial tools. Many consider his way of describing computations in logical theories as seminal in the area of reduction types. With Jesse Wright, identifying automata with algebras he opened them to algebraic treatment. In a book which I edited after his death he deals with the subject, and with its generalization to tree automata and context-free languages, in a uniform way through semi-Thue systems, aiming for a mathematical theory of terms. Less recognized is his concept of “abstraction” for characterizing structures by their automorphism groups, which he considered basic for a theory of definability. An axiomatic theory of convexity which originated therefrom is partly published jointly with W. Fenton. Also partly published is joint work on formalizing computing and complexity on abstract data types with the present author. Unpublished is, and likely will be, his continued work on an algorithmic version of Gauss’ theory of quadratic forms, which stemmed from his interest in Hilbert’s 10th problem. Results in the existential theory of concatenation, which link the two areas, are published jointly with S. Senger. Saunders MacLane and I edited a volume of Collected Works of Richard Büchi.


Turing Machine Diophantine Equation Finite Automaton Winning Strategy Existential Theory 
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Doctoral Students

  1. William Henry Hosken (1966)—Canonical Systems which Produce Regular SetsGoogle Scholar
  2. Lawrence Hugh Landweber (1967)—A Design Algorithm for Sequential Machines and Definability in Monadic Second Order Arithmetic.Google Scholar
  3. Gary Martin Haggard (1968)—Embedding of Graphs in Surfaces.Google Scholar
  4. Kenneth Joe Danhof (1969)—On Definability and the Cantor Method in Model Theory.Google Scholar
  5. Peng-Siu Mei (1971)—Linear Closure Spaces and Matroids, Convex Closure Spaces and Paramatroids.Google Scholar
  6. Jean-Louis Lassez (1973)—On the Relationship Between Prefix Codes, Trees and Automata.Google Scholar
  7. Charles Zaiontz (1974)—Automata and the Monadic Theory of Ordinals < ω2.Google Scholar
  8. Terrence Michael Owens (1975)—Varieties of Skolem Rings.Google Scholar
  9. William Ellis Fenton (1982)—Axiomatic Convexity Theory.Google Scholar
  10. Steven Orville Senger (1982)—The Existential Theory of Concatenation over a Finite Alphabet.Google Scholar

Further Publications

  1. Dirk Siefkes: Grammars for Terms and Automata. On a book by the late J. Richard Büchi. In: Computation Theory and Logic, Egon Börger (ed.), Lect. Notes Comp. Sci., vol. 270 (Rödding memorial volume), Springer-Verlag, New York, 1987, pp. 349–359.Google Scholar
  2. Saunders Maclane, Dirk Siefkes ed.: Collected Works of J. Richard Büchi. Springer-Verlag, New York, 1990.Google Scholar

Copyright information

© Birkhäuser Boston 2008

Authors and Affiliations

  • Dirk Siefkes
    • 1
  1. 1.Institut für Software und Theoretische InformatikTechnische Universität BerlinBerlin 10Germany

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