Concrete Abstractions [electronic resource] : Formalizing and Analyzing Discrete Theories and Algorithms with the RISCAL Model Checker / by Wolfgang Schreiner.

Por: Schreiner, Wolfgang [author.]Colaborador(es): SpringerLink (Online service)Tipo de material: TextoTextoSeries Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, AustriaEditor: Cham : Springer International Publishing : Imprint: Springer, 2023Edición: 1st ed. 2023Descripción: XII, 271 p. 79 illus., 53 illus. in color. online resourceTipo de contenido: text Tipo de medio: computer Tipo de portador: online resourceISBN: 9783031249341Tema(s): Computer science -- Mathematics | Mathematics -- Data processing | Mathematical logic | Mathematics of Computing | Computational Mathematics and Numerical Analysis | Mathematical Logic and FoundationsFormatos físicos adicionales: Printed edition:: Sin título; Printed edition:: Sin título; Printed edition:: Sin títuloClasificación CDD: 004.0151 Clasificación LoC:QA76.9.M35Recursos en línea: Libro electrónicoTexto
Contenidos:
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.
En: Springer Nature eBookResumen: 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.
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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.

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.

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