Titlebook: Concrete Abstractions; Formalizing and Anal Wolfgang Schreiner Textbook 2023 The Editor(s) (if applicable) and The Author(s), under exclusi

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linear

0943-853X 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..978-3-031-24936-5978-3-031-24934-1Series ISSN 0943-853X Series E-ISSN 2197-8409

諷刺

,Theories and?Algorithms,ories, and algorithms that solve these problems. For this purpose, we shall in this chapter focus on the theory of (a certain kind of) numbers, the problem of computing the greatest common divisor (gcd) of two numbers, and the ancient Euclidean algorithm that computes the gcd.

OUTRE

,Searching and?Sorting,rranging the elements in the array in a particular order (such that we may speed up subsequent searches). In the course of our elaboration, we will also discuss the principles of formal program/algorithm verification and how they are supported in RISCAL.

深淵

Sets, Relations, and Graphs,ues. Since sets and relations can model the nodes and arrows of directed “graphs”, we take the opportunity to consider graph problems such as determining the reachability of nodes and the computation of shortest paths.

蟄伏

向前變橢圓

Puzzles and Games,r is dedicated to the “l(fā)ighter” domain of recreational mathematics, which disguises computational problems in the entertaining form of . or .. From the large variety of mathematical games, we will choose some examples that can be naturally represented in the form of discrete systems that have a fini

GROG

Concurrent Systems,tly executing components. Examples of such systems are programs with multiple processes or threads that cooperate via shared variables as well as multiple independent programs that interact by exchanging messages over a network.

暗諷

Further Topics, two recent additions that significantly enhance the capabilities of the software: first, checking specifications of nondeterministic and concurrent systems that are expressed in the language of . and, second, . in domains of arbitrary size.

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