Concrete Abstractions: Formalizing and Analyzing Discrete Theories and Algorithms with the RISCAL Model...

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Wolfgang Schreiner

Concrete Abstractions

Formalizing and Analyzing Discrete Theories and Algorithms with the RISCAL Model Checker

Wolfgang Schreiner

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English

Springer International Publishing AG
12 April 2023

Mathematical foundations; Mathematical logic; Numerical analysis; Mathematical theory of computation; Maths for computer scientists

Series: Texts & Monographs in Symbolic Computation

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.

By: Wolfgang Schreiner
Imprint: Springer International Publishing AG
Country of Publication: Switzerland
Edition: 1st ed. 2023
Dimensions: Height: 235mm, Width: 155mm,
Weight: 594g
ISBN: 9783031249334
ISBN 10: 303124933X
Series: Texts & Monographs in Symbolic Computation
Pages: 271
Publication Date: 12 April 2023
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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.

Wolfgang Schreiner is an associate professor at the Research Institute for Symbolic Computation (RISC) of the Johannes Kepler University Linz, Austria. He is working in formal methods of computer science (with previous research in parallel computing and functional programming), and has produced various software packages related to formal semantics, specification, and verification, in particular the RISC ProofNavigator, the RISC ProgramExplorer, and the RISC Algorithm Language (RISCAL). Formerly he directed a degree programme on Computer-based Learning at the Upper Austria University of Applied Sciences in Hagenberg.