عنوان

Iteration Theories :

شابک

3642780342

شابک

9783642780349

شماره

b573759

عنوان اصلي

Iteration Theories :

نام عام مواد

[Book]

ساير اطلاعات عنواني

the Equational Logic of Iterative Processes

نام نخستين پديدآور

by Stephen L. Bloom, Zoltán Ésik.

محل نشرو پخش و غیره

Berlin, Heidelberg

نام ناشر، پخش کننده و غيره

Springer Berlin Heidelberg

تاریخ نشرو بخش و غیره

1993

نام خاص و کميت اثر

(xv, 630 pages)

عنوان فروست

EATCS monographs on theoretical computer science.

متن يادداشت

1 Mathematical Motivation --; 2 Why Iteration Theories? --; 3 Suggestions for the Impatient Reader --; 4 A Disclaimer --; 5 Numbering --; 1 Preliminary Facts --; 1 Sets and Functions --; 2 Posets --; 3 Categories --; 4 2-Categories --; 4.1 Cellc is a 2-Category, Too --; 5?-Trees --; 2 Varieties and Theories --; 1 S-Algebras --; 2 Terms and Equations --; 3 Theories --; 4 The Theory of a Variety. --; 3 Theory Facts --; 1 Pairing and Separated Sum --; 2 Elementary Properties of TH --; 3 Theories as N x N-Sorted Algebras --; 4 Special Coproducts --; 5 Matrix and Matricial Theories --; 6 Pullbacks and Pushouts of Base Morphisms --; 7 2-Theories --; 4 Algebras --; 1 T-algebras --; 2 Free Algebras in Tb --; 3 Subvarieties of Tb --; 4 The Categories TH and var --; 5 Notes --; 5 Iterative Theories --; 1 Ideal Theories --; 2 Iterative Theories Defined --; 3 Properties of Iteration in Iterative Theories --; 4 Free Iterative Theories --; 5 Notes --; 6 Iteration Theories --; 1 Iteration Theories Defined --; 2 Other Axiomatizations of Iteration Theories --; 3 Theories with a Functorial Dagger --; 4 Pointed Iterative Theories --; 5 Free Iteration Theories --; 6 Constructions on Iteration Theories --; 7 Feedback Theories --; 8 Summary of the Axioms --; 9 Notes --; 7 Iteration Algebras --; 1 Definitions --; 2 Free Algebras in T --; 3 The Retraction Lemma --; 4 Some Categorical Facts --; 5 Properties of T --; 6 A Characterization Theorem --; 7 Strong Iteration Algebras --; 8 Notes --; 8 Continuous Theories --; 1 Ordered Algebraic Theories --; 2?-Continuous Theoriesx --; 3 Rational Theories --; 4 Initiality and Iteration in 2-Theories --; 5?-Continuous 2-Theories --; 6 Notes --; 9 Matrix Iteration Theories --; 1 Notation --; 2 Properties of the Star Operation --; 3 Matrix Iteration Theories Defined --; 4 Presentations in Matrix Iteration Theories --; 5 The Initial Matrix Iteration Theory --; 6 An Extension Theorem --; 7 Matrix Iteration Theories of Regular Sets --; 8 Notes --; 10 Matricial Iteration Theories --; 1 From Dagger to Star and Omega, and Back --; 2 Matricial Iteration Theories Defined --; 3 Examples --; 4 Additively Closed Subiteration Theories --; 5 Presentations in Matricial Iteration Theories --; 6 The Initial Matricial Iteration Theory --; 7 The Extension Theorem --; 8 Additively Closed Theories of Regular Languages --; 9 Closed Regular (?-Languages --; 10 Notes --; 11 Presentations --; 1 Presentations in Iteration Theories --; 2 Simulations of Presentations --; 3 Coproducts Revisited --; 4 Notes --; 12 Flowchart Behaviors --; 1 Axiomatizing Sequacious Functions --; 2 Axiomatizing Partial Functions --; 3 Diagonal Theories --; 4 Sequacious Functions with Predicates --; 5 Partial Functions with Predicates --; 6 Notes --; 13 Synchronization Trees --; 1 Theories of Synchronization Trees --; 2 Grove Iteration Theories --; 3 Axiomatizing Synchronization Trees --; 4 Bisimilarity --; 5 Notes --; 14 Floyd-Hoare Logic --; 1 Guards --; 2 Partial Correctness Assertions --; 3 The Standard Example --; 4 Rules for Partial Correctness --; 5 Soundness --; 6 The Standard Example, Continued --; 7 A Floyd-Hoare Calculus for Iteration Theories --; 8 The Standard Example, Again --; 9 Completeness --; 10 Examples --; 11 Notes --; List of Symbols.

متن يادداشت

Written both for graduate students and research scientists in theoretical computer science and mathematics, this book provides a detailed investigation of the properties of the fixed point or iteration operation. Iteration plays a fundamental role in the theory of computation: for example, in the theory of automata, in formal language theory, in the study of formal power series, in the semantics of flowchart algorithms and programming languages, and in circular data type definitions. It is shown that in all structures that have beenused as semantic models, the equational properties of the fixed point operation are captured by the axioms describing iteration theories. These structures include ordered algebras, partial functions, relations, finitary and infinitary regular languages, trees, synchronization trees, 2-categories, and others. The book begins with a gentle introduction to the study of universal algebra in the framework of algebraictheories. A remarkably useful calculus is developed for manipulating algebraic theory terms. The reader is then guided through a vast terrain of theorems and applications by means of detailed proofs, examples, and exercises, with the emphasis on equational proofs. The last chapter shows that the familiar topic of correctness logic is a special caseof the equational logic of iteration theories. Several significant open problems are scattered throughout the text.

موضوع مستند نشده

Computer science.

موضوع مستند نشده

Logic design.

موضوع مستند نشده

Logic, Symbolic and mathematical.

شماره رده

نشانه اثر

مستند نام اشخاص تاييد نشده

by Stephen L. Bloom, Zoltán Ésik.

مستند نام اشخاص تاييد نشده

Stephen L Bloom

مستند نام اشخاص تاييد نشده

Zoltán Ésik

نام الکترونيکي

نوع ماده

[Book]

تكميل شده

Y