LEADER 02989nam 2200529 450 001 996547958903316 005 20230611131848.0 010 $a9783031249341$b(electronic bk.) 010 $z9783031249334 024 7 $a10.1007/978-3-031-24934-1 035 $a(MiAaPQ)EBC7236307 035 $a(Au-PeEL)EBL7236307 035 $a(OCoLC)1376196151 035 $a(DE-He213)978-3-031-24934-1 035 $a(PPN)269656383 035 $a(EXLCZ)9926428337000041 100 $a20230611d2023 uy 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aConcrete Abstractions $eFormalizing and Analyzing Discrete Theories and Algorithms with the RISCAL Model Checker /$fWolfgang Schreiner 205 $a1st ed. 2023. 210 1$aCham, Switzerland :$cSpringer, Springer Nature Switzerland AG,$d[2023] 210 4$dİ2023 215 $a1 online resource (278 pages) 225 1 $aTexts and Monographs in Symbolic Computation Series 311 08$aPrint version: Schreiner, Wolfgang Concrete Abstractions Cham : Springer International Publishing AG,c2023 9783031249334 320 $aIncludes bibliographical references. 327 $a1. 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. 330 $aThis book demonstrates how to formally model various mathematical domains (including algorithms operating in these domains) in a way that makes them amenable to a fully automatic analysis by computer software. The presented domains are typically investigated in discrete mathematics, logic, algebra, and computer science; they are modeled in a formal language based on first-order logic which is sufficiently rich to express the core entities in whose correctness we are interested: mathematical theorems and algorithmic specifications. This formal language is the language of RISCAL, a ?mathematical model checker? by which the validity of all formulas and the correctness of all algorithms can be automatically decided. The RISCAL software is freely available; all formal contents presented in the book are given in the form of specification files by which the reader may interact with the software while studying the corresponding book material. 410 0$aTexts and monographs in symbolic computation. 606 $aAlgorithms 606 $aMathematical models 606 $aMathematics$xData processing 615 0$aAlgorithms. 615 0$aMathematical models. 615 0$aMathematics$xData processing. 676 $a511.8 700 $aSchreiner$b Wolfgang$f1967-$01236216 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 912 $a996547958903316 996 $aConcrete Abstractions$93390443 997 $aUNISA