Concrete Abstractions

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.

Introduces the main concepts of formal modeling Presents examples related to computer science, set and graph theory, propositional logic, puzzles and games Formulates all examples in the language of the freely available RISCAL model checker

Autorentext
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.

Inhalt

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. <p