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

This book demonstrates how to model mathematical domains in a formal language based on first-order logic, making them amenable to automatic analysis by computer software. The RISCAL software is freely available to check the validity of formulas and the correctness of algorithms.

Format: Hardback
Length: 270 pages
Publication date: 12 April 2023
Publisher: Springer International Publishing AG

This book is a groundbreaking resource that showcases an innovative approach to formally modeling diverse mathematical domains, encompassing algorithms operating within these domains, in a manner that enables them to be thoroughly analyzed by computer software. The modeled domains typically fall under the purview of discrete mathematics, logic, algebra, and computer science, and they are represented in a formal language rooted in first-order logic, which possesses the necessary richness to capture the fundamental entities of interest, such as mathematical theorems and algorithmic specifications. This formal language serves as the backbone of RISCAL, a remarkable "mathematical model checker" that automatically determines the validity of all formulas and the correctness of all algorithms. The remarkable aspect of RISCAL is that it is freely accessible to the public, and the book provides all formal contents in the form of specification files, allowing readers to interact with the software while delving into the corresponding book material. By employing this approach, the book empowers readers to gain a deeper understanding of the mathematical concepts and algorithms presented, while also facilitating the automated verification of their correctness, thus enhancing the reliability and efficiency of software development in these fields.

Weight: 594g
Dimension: 235 x 155 (mm)
ISBN-13: 9783031249334
Edition number: 1st ed. 2023