Binary Functions and their Applications

In this book representations of binary functions by implicants and implicates are deduced. The results are applied to describe the reliability of technical systems and to classification problems, and to an important class of finite Boolean algebras.

Contenu

1. Introduction.- 2. Binary Functions and their Representations by Implicants.- 2.1 Cube Indicators.- 2.2 Implicants.- 2.3 Prime Implicants.- 2.4 Representations by Implicants (Prime Implicants).- 3. Representations of Binary Functions by Implicates.- 3.1 Anticube Indicators.- 3.2 Implicates.- 3.3 Prime Implicates.- 3.4 Representations by Implicates (Prime Implicates).- 4. Reduction Methods.- 4.1 Notation.- 4.2 Rule.- 4.3 Rule.- 4.4 Rule.- 4.5 Rule.- 4.6 Rule.- 4.7 Rule (Corollary).- 4.8 Rule.- 4.9 Rule.- 5. Discrete Functions.- 5.1 Representations by Binary Functions.- 5.2 Monotone Functions.- 5.3 Semimonotone Functions.- 5.4 Implicants (Prime Implicants) of Discrete Functions.- 5.5 Representations by Implicants (Prime Implicants).- 5.6 Implicates (Prime Implicates) of Discrete Functions.- 5.7 Representations by Implicates (Prime Implicates).- 6. Applications.- 6.1 Reliability Structure of Technical Systems.- 6.2 Classification (Valuation) of Objects.- 7. A Class of Finite Boolean Algebras.- 7.1 Boolean Algebras.- 7.2 Boolean Algebras Generated by Finite Partitions.- 7.3 Representations of Boolean Elements by Implicants.- 7.4 Representations of Boolean Elements by Implicates.- 7.5 Probability.- 8. Applications.- 8.1 Set Algebras (Event Algebras).- 8.2 Indicator Algebras.- 8.3 Partitions in Propositional Logic.- 8.4 Algebras of Classes of Propositions.- 8.5 Truth Function Algebras.- 8.6 Some Related Models.- 8.7 Calculation of Elements of B*.- Concluding Remark.- References.- List of Symbols.