Concrete Abstractions Formalizing and Analyzing Discrete Theories and Algorithms with the RISCAL Model Checker /
Schreiner, Wolfgang.
Concrete Abstractions Formalizing and Analyzing Discrete Theories and Algorithms with the RISCAL Model Checker / [electronic resource] : by Wolfgang Schreiner. - 1st ed. 2023. - XII, 271 p. 79 illus., 53 illus. in color. online resource. - Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, 2197-8409 . - Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, .
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.
9783031249341
10.1007/978-3-031-24934-1 doi
Computer science--Mathematics.
Mathematics--Data processing.
Mathematical logic.
Mathematics of Computing.
Computational Mathematics and Numerical Analysis.
Mathematical Logic and Foundations.
QA76.9.M35
004.0151
Concrete Abstractions Formalizing and Analyzing Discrete Theories and Algorithms with the RISCAL Model Checker / [electronic resource] : by Wolfgang Schreiner. - 1st ed. 2023. - XII, 271 p. 79 illus., 53 illus. in color. online resource. - Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, 2197-8409 . - Texts & Monographs in Symbolic Computation, A Series of the Research Institute for Symbolic Computation, Johannes Kepler University, Linz, Austria, .
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.
9783031249341
10.1007/978-3-031-24934-1 doi
Computer science--Mathematics.
Mathematics--Data processing.
Mathematical logic.
Mathematics of Computing.
Computational Mathematics and Numerical Analysis.
Mathematical Logic and Foundations.
QA76.9.M35
004.0151