## Quick Reference

*S** ^{m}* (see Cartesian product) into

*S*itself, where

*S*is some set specific to the function. Such a function is usually referred to as an

*m*-ary or

*m*-adic operation over

*S*,

*m*being some natural number, sometimes referred to as the

**arity**of the operation. The most common operations are the dyadic (or binary) operations that map

*S*×

*S*into

*S*and the monadic (or unary) operations that map

*S*into

*S*. The case where the arity is zero gives the so-called

**nullary**operations, which correspond simply to elements of

*S*. There is also a more general kind of operation that involves more than one set. For example, in a finite-state automaton the next state depends on the current input symbol and the current state, and is thus given by a dyadic operation from

*I*×

*Q*into

*Q*, where

*I*is the set of input symbols and

*Q*the set of states. See also logic operation, arithmetic operation, operations on sets.

*Another name for* instruction (in a computer), as designated by an operation code.

**From:**
operation
in
A Dictionary of Computing »

*Subjects:*
Computing.

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