complexity measure
complexity measure A means of measuring the resources used during a computation. A general definition is contained in Blum's axioms. In the special case of Turing machines, during any Turing machine computation various resources will be used, e.g. space and time. These can be defined formally as follows.
Given a Turing machine program M and an input string x, then Time(M,x) is defined as the number of steps in the computation of M on x before M halts. Time is undefined if M does not halt on x. The time complexity of M is defined to be the integer function TM where TM(n) = max(Time(M,x): |x| = n)
for nonnegative integer n.
Space(M,x) is similarly defined as the number of tape squares used by M on x, and the space complexity SM is defined by SM(n) = max(Space(M,x): |x| = n)
However, in order to distinguish the space required for working as opposed to the space for the input string x, the machine is sometimes considered as having a read-only input tape, and Space(M,x) is defined as the number of squares used by M on x.
The more general measures of complexity share many of the common properties of time and space (see Blum's axioms).
An algorithm for which the complexity measure TM(n) or SM(n) increases with n no more rapidly than a polynomial in n is said to be polynomially bounded; one in which it grows exponentially is said to be exponentially bounded.
See also complexity classes.
Given a Turing machine program M and an input string x, then Time(M,x) is defined as the number of steps in the computation of M on x before M halts. Time is undefined if M does not halt on x. The time complexity of M is defined to be the integer function TM where TM(n) = max(Time(M,x): |x| = n)
for nonnegative integer n.
Space(M,x) is similarly defined as the number of tape squares used by M on x, and the space complexity SM is defined by SM(n) = max(Space(M,x): |x| = n)
However, in order to distinguish the space required for working as opposed to the space for the input string x, the machine is sometimes considered as having a read-only input tape, and Space(M,x) is defined as the number of squares used by M on x.
The more general measures of complexity share many of the common properties of time and space (see Blum's axioms).
An algorithm for which the complexity measure TM(n) or SM(n) increases with n no more rapidly than a polynomial in n is said to be polynomially bounded; one in which it grows exponentially is said to be exponentially bounded.
See also complexity classes.
More From encyclopedia.com
Lysithea , Lysithea (Jupiter X) One of the lesser satellites of Jupiter, with a diameter of 24km. Diophantus Of Alexandria , Diophantus of Alexandria
Diophantus of Alexandria
(fl. ad. 250)
mathematics.
We know virtually nothing about the life of Diophantus. The dating of hi… Inverse Matrix , Inverse Matrix
BIBLIOGRAPHY
The concept of inverse matrix is somewhat analogous to that of the reciprocal of a number. If a is a nonzero number, then… Differential Equations , Differential equations
Differential equations are models of real systems that are believed to change their states continuously, or, to put it more pr… Exponent , Skip to main content
exponent
exponent •abeyant, mayn't •ambient, circumambient •gradient, irradiant, radiant •expedient, ingredient, mediant, obedie… Equation , equation An expression that asserts the equality of two terms. To be precise, an equation has the following form. Let Σ be a signature and let t1(X1,…
You Might Also Like
NEARBY TERMS
complexity measure