Rudiments of Calculus

Przednia okładka
A. Arnold, D. Niwinski
Elsevier, 7 lut 2001 - 298

This book presents what in our opinion constitutes the basis of the theory of the mu-calculus, considered as an algebraic system rather than a logic. We have wished to present the subject in a unified way, and in a form as general as possible. Therefore, our emphasis is on the generality of the fixed-point notation, and on the connections between mu-calculus, games, and automata, which we also explain in an algebraic way.

This book should be accessible for graduate or advanced undergraduate students both in mathematics and computer science. We have designed this book especially for researchers and students interested in logic in computer science, comuter aided verification, and general aspects of automata theory. We have aimed at gathering in a single place the fundamental results of the theory, that are currently very scattered in the literature, and often hardly accessible for interested readers.

The presentation is self-contained, except for the proof of the Mc-Naughton's Determinization Theorem (see, e.g., [97]. However, we suppose that the reader is already familiar with some basic automata theory and universal algebra. The references, credits, and suggestions for further reading are given at the end of each chapter.

 

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Spis treści

Chapter 1 Complete lattices and fixedpoint theorems
1
Syntax and semantics
41
Chapter 3 The Boolean μcalculus
71
Chapter 4 Parity games
85
Chapter 5 The μcalculus on words
105
Chapter 6 The μcalculus over powerset algebras
141
Chapter 7 The μcalculus vs automata
155
Chapter 8 Hierarchy problems
191
Chapter 9 Distributivity and normal form results
205
Chapter 10 Decision problems
233
Chapter 11 Algorithms
253
Bibliography
269
Index
275
Prawa autorskie

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Popularne fragmenty

Strona 269 - References 1. HR. Andersen. Model checking and boolean graphs. Theoretical Computer Science, 126:3-30, 1994. 2. A. Arnold and P. Crubille. A linear time algorithm to solve fixed-point equations on transition systems.
Strona 5 - L6 . x A (y V z) = (x A y) V (x A z) L6".
Strona 273 - Bart Vergauwen and Johan Lewi. A linear algorithm for solving fixed-point equations on transition systems. In J.-C. Raoult, editor, Proceedings of 17'th Colloquium on Trees in Algebra and Programming, CAAP'92, Rennes, France, volume 581 of LNCS, pages 322-341. Springer- Verlag, 1992.
Strona 269 - Fixed point characterization of Buchi automata on infinite trees. J. Inf. Process. Cybern.

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