Concrete Abstractions : Formalizing and Analyzing Discrete Theories and Algorithms with the RISCAL Model Checker (Texts & Monographs in Symbolic Computation) （2023）

Schreiner, Wolfgang

Springer International Publishing AG（2023/04発売）

• 製本 Hardcover:ハードカバー版／ページ数 271 p.
• 言語 ENG
• 商品コード 9783031249334
• DDC分類 511.8

Full Description

This book demonstrates how to formally model various mathematical domains (including algorithms operating in these domains) in a way that makes them amenable to a fully automatic analysis by computer software.The presented domains are typically investigated in discrete mathematics, logic, algebra, and computer science; they are modeled in a formal language based on first-order logic which is sufficiently rich to express the core entities in whose correctness we are interested: mathematical theorems and algorithmic specifications. This formal language is the language of RISCAL, a "mathematical model checker" by which the validity of all formulas and the correctness of all algorithms can be automatically decided. The RISCAL software is freely available; all formal contents presented in the book are given in the form of specification files by which the reader may interact with the software while studying the corresponding book material.

Contents

1. Theories and Algorithms.- 2. Searching and Sorting.- 3. Sets, Relations, and Graphs.- 4. Propositional Logic.- 5. Big Number and Polynomial Arithmetic.- 6. Puzzles and Games.- 7. Concurrent Systems.- 8. Further Topics.- Appendices.- References.- Index.