By Yves Crama, Peter L. Hammer
This choice of papers provides a sequence of in-depth examinations of numerous complex themes on the topic of Boolean services and expressions. The chapters are written via one of the most fashionable specialists of their respective fields and canopy issues starting from algebra and propositional common sense to studying concept, cryptography, computational complexity, electric engineering, and reliability thought. past the variety of the questions raised and investigated in several chapters, a striking characteristic of the gathering is the typical thread created by means of the elemental language, techniques, versions, and instruments supplied by way of Boolean thought. Many readers could be stunned to find the numerous hyperlinks among probably distant subject matters mentioned in quite a few chapters of the publication. this article is going to aid them draw on such connections to extra their realizing in their personal clinical self-discipline and to discover new avenues for examine.
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Additional info for Boolean Models and Methods in Mathematics, Computer Science, and Engineering
It is natural to ask about the intersection i=2 Polμi . It can be shown that it is the clone → . This clone consists of functions that can be built from → alone, such as, g(x, y, z) :≈ (y → z) → x ≈ x ∨ yz . In fact, the clone → and seven other related clones are the only clones not of the form Polρ for a (finitary) relation ρ on B. A good part of the calculus of the 2-valued propositional logic studies certain properties of the clone → . For example, an n-ary tautology based only on → expresses a way the n-ary constant c1n is composed from →.
16–29, 1970. P. Camion. Une m´ethode de r´esolution par l’alg`ebre de Boole des probl`emes combinatoires o`u interviennent des entiers. Cahiers du Centre d’Etudes de Recherche Op´erationnelle 2, pp. 234–89, 1960. Y. Crama, and P. L. Hammer. Boolean Functions: Theory, Algorithms, and Applications. Cambridge University Press, Cambridge, UK, 2010. S. G. Gindikin. Algebra of Logic (Russian). Nauka 1972. English translation: Algebraic Logic, Springer-Verlag, 1985. S. V. Iablonski˘i. On the superposition of functions of algebra of logic (Russian).
An ) ≤ f (b1 , . . , bn ); that is, if every argument is kept the same or increased, then the value is the same or increases. This is the standard definition of a monotone (also isotone, order-respecting, or order-compatible) Boolean function; see . 5. 1. Expressed differently, the last where + coordinate in a 4-tuple from λ is exactly the parity check (making the coordinate sum even), a basic error check used in computer hardware and other digital devices; equivalently, a 4-tuple belongs to λ if and only if it contains an even number of 1s.
Boolean Models and Methods in Mathematics, Computer Science, and Engineering by Yves Crama, Peter L. Hammer