Büchi, J. Richard
Overview
Works:  23 works in 99 publications in 2 languages and 1,089 library holdings 

Roles:  Author 
Classifications:  QA3, 511.3 
Publication Timeline
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Most widely held works about
J. Richard Büchi
 The collected works of J. Richard Büchi by J. Richard Büchi( Book )
 Büchi's monadic second order successor arithmetic by Dirk Siefkes( Book )
Most widely held works by
J. Richard Büchi
The monadic second order theory of all countable ordinals by
J. Richard Büchi(
Book
)
25 editions published in 1973 in English and held by 381 WorldCat member libraries worldwide
25 editions published in 1973 in English and held by 381 WorldCat member libraries worldwide
Finite automata, their algebras and grammars : towards a theory of formal expressions by
J. Richard Büchi(
Book
)
14 editions published between 1988 and 2012 in English and held by 272 WorldCat member libraries worldwide
The author, who died in 1984, is wellknown both as a person and through his research in mathematical logic and theoretical computer science. In the first part of the book he presents the new classical theory of finite automata as unary algebras which he himself invented about 30 years ago. Many results, like his work on structure lattices or his characterization of regular sets by generalized regular rules, are unknown to a wider audience. In the second part of the book he extends the theory to general (nonunary, manysorted) algebras, term rewriting systems, tree automata, and pushdown automata. Essentially Büchi worked independent of other rersearch, following a novel and stimulating approach. He aimed for a mathematical theory of terms, but could not finish the book. Many of the results are known by now, but to work further along this line presents a challenging research program on the borderline between universal algebra, term rewriting systems, and automata theory. For the whole book and again within each chapter the author starts at an elementary level, giving careful explanations and numerous examples and exercises, and then leads up to the research level. In this way he covers the basic theory as well as many nonstandard subjects. Thus the book serves as a textbook for both the beginner and the advances student, and also as a rich source for the expert
14 editions published between 1988 and 2012 in English and held by 272 WorldCat member libraries worldwide
The author, who died in 1984, is wellknown both as a person and through his research in mathematical logic and theoretical computer science. In the first part of the book he presents the new classical theory of finite automata as unary algebras which he himself invented about 30 years ago. Many results, like his work on structure lattices or his characterization of regular sets by generalized regular rules, are unknown to a wider audience. In the second part of the book he extends the theory to general (nonunary, manysorted) algebras, term rewriting systems, tree automata, and pushdown automata. Essentially Büchi worked independent of other rersearch, following a novel and stimulating approach. He aimed for a mathematical theory of terms, but could not finish the book. Many of the results are known by now, but to work further along this line presents a challenging research program on the borderline between universal algebra, term rewriting systems, and automata theory. For the whole book and again within each chapter the author starts at an elementary level, giving careful explanations and numerous examples and exercises, and then leads up to the research level. In this way he covers the basic theory as well as many nonstandard subjects. Thus the book serves as a textbook for both the beginner and the advances student, and also as a rich source for the expert
Decidable Theories II : The Monadic Second Order Theory of All Countable Ordinals by
J. Richard Büchi(
)
7 editions published in 1973 in English and held by 34 WorldCat member libraries worldwide
7 editions published in 1973 in English and held by 34 WorldCat member libraries worldwide
Die Boole'sche partialordnung und die paarung von Gefugen by
J. Richard Büchi(
Book
)
9 editions published in 1950 in German and held by 30 WorldCat member libraries worldwide
9 editions published in 1950 in German and held by 30 WorldCat member libraries worldwide
The collected works of J. Richard Büchi by
J. Richard Büchi(
Book
)
8 editions published between 1990 and 2012 in English and held by 25 WorldCat member libraries worldwide
8 editions published between 1990 and 2012 in English and held by 25 WorldCat member libraries worldwide
Manual on REC by
J. Richard Büchi(
Book
)
4 editions published in 1984 in 3 languages and held by 7 WorldCat member libraries worldwide
4 editions published in 1984 in 3 languages and held by 7 WorldCat member libraries worldwide
Büchi's monadic second order successor arithmetic by
Dirk Siefkes(
Book
)
1 edition published in 1970 in English and held by 5 WorldCat member libraries worldwide
1 edition published in 1970 in English and held by 5 WorldCat member libraries worldwide
Die Boole'sche Partialordnung und die Paarung von Gefügen by
J. Richard Büchi(
)
1 edition published in 1950 in German and held by 3 WorldCat member libraries worldwide
1 edition published in 1950 in German and held by 3 WorldCat member libraries worldwide
Regular canonical systems and finite automata by
J. Richard Büchi(
Book
)
3 editions published in 1959 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1959 in English and held by 2 WorldCat member libraries worldwide
Weak secondorder arithmetic and finite automata by
J. Richard Büchi(
Book
)
2 editions published in 1959 in English and held by 2 WorldCat member libraries worldwide
The formalism of regular expressions was introduced to obtain the following basic theorems: Synthesis  To every regular expression E one can effectively obtain a finite automata A with binary output U such that E denotes the behavior of <A, U>; Analysis  To every finite automaton A with binary output U one can effectively construct a regular expression E such that the behavior of <A, U> is denoted by E. It is shown that a more conventional formalism, a weak secondorder arithmetic, can be used in place of the formalism of regular expressions. This result is of interest for automata theory because formulas of weak secondorder arithmetic seem to be more convenient than regular expressions for formalizing conditions on the behavior of automata. In addition, our synthesis and analysis theorems yield rather complete information on the strength of weak secondorder arithmetic, thus providing an example of applying automata theory to logic. (Author)
2 editions published in 1959 in English and held by 2 WorldCat member libraries worldwide
The formalism of regular expressions was introduced to obtain the following basic theorems: Synthesis  To every regular expression E one can effectively obtain a finite automata A with binary output U such that E denotes the behavior of <A, U>; Analysis  To every finite automaton A with binary output U one can effectively construct a regular expression E such that the behavior of <A, U> is denoted by E. It is shown that a more conventional formalism, a weak secondorder arithmetic, can be used in place of the formalism of regular expressions. This result is of interest for automata theory because formulas of weak secondorder arithmetic seem to be more convenient than regular expressions for formalizing conditions on the behavior of automata. In addition, our synthesis and analysis theorems yield rather complete information on the strength of weak secondorder arithmetic, thus providing an example of applying automata theory to logic. (Author)
ON A PROBLEM OF TARSKI by
J. Richard Büchi(
Book
)
3 editions published in 1960 in English and held by 2 WorldCat member libraries worldwide
3 editions published in 1960 in English and held by 2 WorldCat member libraries worldwide
Definability in the monadic secondorder theory of successor by
J. Richard Büchi(
Book
)
2 editions published in 1967 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1967 in English and held by 2 WorldCat member libraries worldwide
Solving sequential conditions by finite state strategies by
J. Richard Büchi(
Book
)
2 editions published in 1967 in English and held by 2 WorldCat member libraries worldwide
2 editions published in 1967 in English and held by 2 WorldCat member libraries worldwide
Turingmachines and the entscheidungsproblem; technical report by
J. Richard Büchi(
Book
)
3 editions published in 1961 in English and held by 2 WorldCat member libraries worldwide
A discussion of decision theory by use of Turingmachines is presented and is determined to be closely related to the quantification theory. Postulates are stated and application of sentence structure is examined by use of recursive logic methods
3 editions published in 1961 in English and held by 2 WorldCat member libraries worldwide
A discussion of decision theory by use of Turingmachines is presented and is determined to be closely related to the quantification theory. Postulates are stated and application of sentence structure is examined by use of recursive logic methods
Mathematical theory of Automata by
J. Richard Büchi(
Book
)
1 edition published in 1960 in English and held by 2 WorldCat member libraries worldwide
1 edition published in 1960 in English and held by 2 WorldCat member libraries worldwide
Decidable theories by
Dirk Siefkes(
Book
)
1 edition published in 1973 in Undetermined and held by 1 WorldCat member library worldwide
1 edition published in 1973 in Undetermined and held by 1 WorldCat member library worldwide
The collected works of J. Richard Büchi by
J. Richard Büchi(
)
in English and held by 1 WorldCat member library worldwide
in English and held by 1 WorldCat member library worldwide
The monadic secondorder theory of [omega] by
J. Richard Büchi(
Book
)
2 editions published in 1971 in English and held by 1 WorldCat member library worldwide
2 editions published in 1971 in English and held by 1 WorldCat member library worldwide
Verschiedene kleinere Veröffentlichungen aus dem Gebiet der Mathematik(
Book
)
in German and held by 1 WorldCat member library worldwide
in German and held by 1 WorldCat member library worldwide
The monadic order theory of all countable ordinals by
J. Richard Büchi(
Book
)
1 edition published in 1973 in English and held by 1 WorldCat member library worldwide
1 edition published in 1973 in English and held by 1 WorldCat member library worldwide
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Related Identities
 Siefkes, Dirk Other Author Editor
 Mac Lane, Saunders 19092005 Other Editor
 Müller, G. H. Author Editor
 Müller, Gert Heinz
 University of Michigan Department of Philosophy
 Landweber, Lawrence H.
 Mahr, Bernd 1945
 Siefkres, Dirk
 University of Michigan Office of Research Administration
 MICHIGAN UNIV ANN ARBOR
Useful Links
Associated Subjects
Algebra, Abstract ArithmeticFoundations Büchi, J. Richard Computer science Computer software Electronic data processing Gödel's theorem Logic, Symbolic and mathematical Logic design Machine theory Mathematics Model theory Predicate calculus Recursion theory Sequential machine theory Statistical decision
Alternative Names
Büchi, J. R.
Buchi, J. R. 19241984
Büchi, J. Richard 19241984
Büchi, Julius R. 19241984
Büchi, Julius Richard
Büchi, Richard
Büchi, Richard 19241984
Buechi, J.Richard 19241984
Buechi, Julius Richard 19241984
Buechi, Richard J. 19241984
Julius Richard Büchi Schweizer Logiker und Mathematiker
Julius Richard Büchi schweizisk matematiker
Julius Richard Büchi sveitsisk matematikar
Julius Richard Büchi sveitsisk matematiker
Julius Richard Büchi Swiss mathematician
Julius Richard Büchi Zwitsers wiskundige
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