1 Storage Allocation in Program Schemas.- 1.- Descriptive Analysis of the Problem.- 1.1. Brief Review of Computer Programming.- 1.2. Some Facts About Linear Programs.- 1.3. Some Facts About the General Form of a Program.- 1.4. Summary.- 2.- Statement of the Problem and General Theory.- 2.1 Brief Review of Mathematical Foundations.- 2.2. Initial Definitions.- 2.3. General Theory.- 3.- Algorithmization.- 3.1. Data Flow Graph.- 3.2. Incompatibility Graph.- 3.3. Coloring the Vertices of a Graph. General Remarks.- 3.4. Coloring the Vertices of a Graph. The Search for an Algorithm.- 4.- Implementation.- 4.1. Introduction.- 4.2. Structured Programming.- 4.3. General Organization of the Storage Packing Process.- 4.4. Canonical Storage allocation.- 4.5. Creating the Incompatibility Graph.- 4.6. Coloring the Vertices of a Graph.- 5.- Concluding Analysis.- 5.1. The Relationship Between Theory and Practice.- 5.2. Historical Survey.- II Transformations of Yanov Schemas.- 6.- Brief Review of Mathematical Logic.- 6.1. Logical Formulas and Boolean Functions.- 6.2. Algebraic Logic.- 6.3. Propositional Calculus.- 7.- Yanov Schemas.- 7.1. Initial Observations.- 7.2. Search for Basic Definitions.- 7.3. Equivalence of Yanov Schemas.- 8.- Calculus of Equivalence Transformations.- 8.1. Construction of Calculus.- 8.2. Well-Formedness of the Calculus.- 8.3. Canonical Schemas and Technical Theorems.- 8.4. Completeness of Calculus.- 8.5. A Final Historical Survey.
The book begins with a detailed discussion of two problems that have played an extremely important role in the emergence of theoretical programming as an independent discipline. The principal goals in this book are to explain the line of thought that was followed in solving these problems, demonstrate the workings of the mathematical way of thinking, carefully analyze the different stages of descriptive analysis and problem formulation, and reveal the aesthetic component in the search for solutions - in other words, to try to turn the reader into a true witness of the process of discovering mathematical results. In the first part of the book the author considers the storage minimization packing, or storage problem schemas. The problem of storage packing is treated as an example that illustrates how to solve an application problem by means of mathematical methods. In the second part the author presents the theory of Yanov program schemas, a classical theory generally recognized as having served as a foundation of the mathematical theory of programming. This is analyzed as a methodological example that illustrates how a fully developed theory can be extended to a new class of phenomena and objects: program schemas and configurations of program schemas.
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