definitions of a time-constructible function. In the first definition, a function f {\displaystyle f} is called time-constructible if there exists a Turing...

coordinate system, a point is constructible if and only if its Cartesian coordinates are both constructible numbers. Constructible numbers and points have also...

is constructible if any root of the nth cyclotomic polynomial is constructible. Restating the Gauss–Wantzel theorem: A regular n-gon is constructible with...

In mathematics, in set theory, the constructible universe (or Gödel's constructible universe), denoted by L , {\displaystyle L,} is a particular class...

B over A Constructible universe, Kurt Gödel's model L of set theory, constructed by transfinite recursion Constructible function, a function whose values...

The axiom of constructibility is a possible axiom for set theory in mathematics that asserts that every set is constructible. The axiom is usually written...

assumed. □ The above theorem implies the necessity of the space-constructible function assumption in the space hierarchy theorem. L = DSPACE(O(log n))...

notion of a time-constructible function. A function f : N → N {\displaystyle f:\mathbb {N} \rightarrow \mathbb {N} } is time-constructible if there exists...

common functions that we work with are space-constructible, including polynomials, exponents, and logarithms. For every space-constructible function f :...

mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the...

sorted array sorted list sort in-place sort merge soundex space-constructible function spanning tree sparse graph sparse matrix sparsification sparsity...

mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions) are real functions which relate an angle of...

mathematics, the gamma function (represented by Γ, capital Greek letter gamma) is the most common extension of the factorial function to complex numbers....

NTIME is also related to DSPACE in the following way. For any time constructible function t(n), we have N T I M E ( t ( n ) ) ⊆ D S P A C E ( t ( n ) ) {\displaystyle...

A hash function is any function that can be used to map data of arbitrary size to fixed-size values, though there are some hash functions that support...

complexity functions, then f + g, fg, and 2f are also proper complexity functions. Similar notions include honest functions, space-constructible functions, and...

are constructible, and all constructible numbers are algebraic. There are numbers such as the cube root of 2 which are algebraic but not constructible. The...

all prime numbers, the set of all rational numbers, the set of all constructible numbers (in the geometric sense), the set of all algebraic numbers,...

In algebraic geometry, the Behrend function of a scheme X, introduced by Kai Behrend, is a constructible function ν X : X → Z {\displaystyle \nu _{X}:X\to...

optimization and decision theory, a loss function or cost function (sometimes also called an error function) is a function that maps an event or values of one...

In quantum physics, a wave function (or wavefunction) is a mathematical description of the quantum state of an isolated quantum system. The most common...

The function assigning to α {\displaystyle \alpha } the α {\displaystyle \alpha } th level L α {\displaystyle L_{\alpha }} of Godel's constructible hierarchy...

mathematical analysis, the Dirac delta function (or δ distribution), also known as the unit impulse, is a generalized function on the real numbers, whose value...

worst cases Busy beaver Circuit complexity Constructible function Cook-Levin theorem Exponential time Function problem Linear time Linear speedup theorem...

formula 7.2) extended the formula to constructible sheaves over a curve (Raynaud 1965). Suppose that F is a constructible sheaf over a genus g smooth projective...

pairing function, and π 1 , π 2 {\displaystyle \pi _{1},\pi _{2}} be its projection functions for inversion. Theorem: Any function constructible via the...

cumulative distribution function (CDF) of a real-valued random variable X {\displaystyle X} , or just distribution function of X {\displaystyle X} ,...

In mathematics, theta functions are special functions of several complex variables. They show up in many topics, including Abelian varieties, moduli spaces...

computer programming, a function object is a construct allowing an object to be invoked or called as if it were an ordinary function, usually with the same...

In mathematics, a Green's function (or Green function) is the impulse response of an inhomogeneous linear differential operator defined on a domain with...