Boolean Functions in Applications
A Boolean function describes how to determine a Boolean value output based on some logical calculation from Boolean inputs. Such functions play a basic role in questions of complexity theory as well as the design of circuits and chips for digital computers. The properties of Boolean functions play a critical role in cryptography, particularly in the design of symmetric key algorithms (see substitution box).
Boolean functions are often represented by sentences in propositional logic, and sometimes as multivariate polynomials over GF(2), but more efficient representations are binary decision diagrams (BDD), negation normal forms, and propositional directed acyclic graphs (PDAG).
In cooperative game theory, monotone Boolean functions are called simple games (voting games); this notion is applied to solve problems in social choice theory.
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Famous quotes containing the word functions:
“When Western people train the mind, the focus is generally on the left hemisphere of the cortex, which is the portion of the brain that is concerned with words and numbers. We enhance the logical, bounded, linear functions of the mind. In the East, exercises of this sort are for the purpose of getting in tune with the unconscious—to get rid of boundaries, not to create them.”
—Edward T. Hall (b. 1914)