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Type of computational problem
In computational complexity theory, a function problem is a computational problem where a single output is expected for every input, but the output is
Function_problem
theory, Tarski's exponential function problem asks whether the theory of the real numbers together with the exponential function is decidable. Alfred Tarski
Tarski's exponential function problem
Tarski's_exponential_function_problem
Shape containing unit line segments in all directions
this work. A modern way of approaching this problem is to consider a particular type of maximal function, which we construct as follows: Denote Sn−1 ⊂
Kakeya_set
Search problem in quantum mechanics
linear function problem, is a search problem that generalizes the Bernstein–Vazirani problem. In the Bernstein–Vazirani problem, the hidden function is implicitly
Hidden linear function problem
Hidden_linear_function_problem
Yes/no problem in computer science
function problem can be turned into a decision problem; the decision problem is just the graph of the associated function. (The graph of a function f
Decision_problem
Concept in theoretical computer science
the functions Σ(n) and S(n) eventually become larger than any computable function. This has implications in computability theory, the halting problem, and
Busy_beaver
Inherent difficulty of computational problems
are encoded as binary strings. A function problem is a computational problem where a single output (of a total function) is expected for every input, but
Computational complexity theory
Computational_complexity_theory
Seven mathematical problems with a US$1 million prize for each solution
to each problem. The Clay Mathematics Institute officially designated the title Millennium Problem for the seven unsolved mathematical problems, the Birch
Millennium_Prize_Problems
Problem in computer science
possible program–input pairs. The problem comes up often in discussions of computability since it demonstrates that some functions are mathematically definable
Halting_problem
Mathematical function that can be computed by a program
computable functions. In computational complexity theory, the problem of computing the value of a function is known as a function problem, by contrast
Computable_function
Problem a computer might be able to solve
represented by their objective function and their constraints. In a function problem a single output (of a total function) is expected for every input,
Computational_problem
Theoretical problem in quantum physics
unsolved problem. Hugh Everett's many-worlds interpretation attempts to solve the problem by suggesting that there is only one wave function, the superposition
Measurement_problem
Set of problems in computational complexity theory
complexity classes defined in terms of other types of problems (e.g. counting problems and function problems) and using other models of computation (e.g. probabilistic
Complexity_class
Problem of finding the best feasible solution
countable set. A problem with continuous variables is known as a continuous optimization, in which an optimal value from a continuous function must be found
Optimization_problem
Topics referred to by the same term
Iamsu! & Problem "Function", song by Dana Kletter from Boneyard Beach 1995 Function (biology), the effect of an activity or process Function (engineering)
Function
Open problem on 3x+1 and x/2 functions
of the unaltered function f defined in the Statement of the problem section of this article). When the relation 3n + 1 of the function f is replaced by
Collatz_conjecture
Study of mathematical algorithms for optimization problems
In the more general approach, an optimization problem consists of maximizing or minimizing a real function by systematically choosing input values from
Mathematical_optimization
Method of solution to differential equations
where δ {\displaystyle \delta } is Dirac's delta function; the solution of the inhomogeneous problem L y = f {\displaystyle Ly=f} is the convolution,
Green's_function
Physics problem related to laws of motion and gravity
In physics, specifically classical mechanics, the three-body problem is to take the initial positions and velocities (or momenta) of three point masses
Three-body_problem
Complexity class
the set of function problems that can be solved by a deterministic Turing machine in polynomial time (and for which the function problem also represents
FP_(complexity)
Programming language implementation problem
science, the funarg problem (function argument problem) refers to the difficulty in implementing first-class functions (functions as first-class objects)
Funarg_problem
Process of calculating the causal factors that produced a set of observations
data misfit function. Some authors have investigated the possibility of reformulating the inverse problem so as to make the objective function less chaotic
Inverse_problem
English expression, used as a response to thanks
No problem is an English expression, used as a response to thanks (among other functions). It is regarded by some as a less formal alternative to you're
No_problem
Process of achieving a goal by overcoming obstacles
Problem solving is the process of achieving a goal by overcoming obstacles, a frequent part of most activities. Problems in need of solutions range from
Problem_solving
Principle in mathematical optimization
problems are optimization problems in which the objective function and the constraints are all linear. In the primal problem, the objective function is
Duality_(optimization)
Conjecture on zeros of the zeta function
Unsolved problem in mathematics Do all non-trivial zeros of the Riemann zeta function have a real part equal to one half? More unsolved problems in mathematics
Riemann_hypothesis
Mathematical relation assigning a probability event to a cost
with the event. An optimization problem seeks to minimize a loss function. An objective function is either a loss function or its opposite (in specific domains
Loss_function
Family of solutions to related differential equations
Bessel functions are a class of special functions that commonly appear in problems involving wave motion, heat conduction, and other physical phenomena
Bessel_function
computational complexity theory, the complexity class FL is the set of function problems that can be solved by a deterministic Turing machine in a logarithmic
FL_(complexity)
23 mathematical problems stated in 1900
the functions defining the group. Mathematical treatment of the axioms of physics. Irrationality and transcendence of certain numbers. Problems of prime
Hilbert's_problems
Set of all things that may be the input of a mathematical function
\mathbb {R} ^{n}} where a problem is posed, making it both an analysis-style domain and also the domain of the unknown function(s) sought. For example,
Domain_of_a_function
Association of one output to each input
recursive function as input and tests whether 0 belongs to its domain of definition (see Halting problem). A multivariate function, multivariable function, or
Function_(mathematics)
Complexity class
set of the counting problems associated with the decision problems in the set NP. More formally, #P is the class of function problems of the form "compute
♯P
Complexity class
class of total function problems that can be solved in nondeterministic polynomial time. That is, it is the class of function problems that are guaranteed
TFNP
Function used as a performance test problem for optimization algorithms
the Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is used as a performance test problem for optimization
Rosenbrock_function
Function used in computer cryptography
Unsolved problem in computer science Do one-way functions exist? More unsolved problems in computer science In computer science, a one-way function is a function
One-way_function
About polynomials in several variables
polynomial function from an n {\displaystyle n} -dimensional space to itself has a Jacobian determinant that is a non-zero constant, then the function has a
Jacobian_conjecture
polynomial? Connes embedding problem in Von Neumann algebra theory Crouzeix's conjecture: the matrix norm of a complex function f {\displaystyle f} applied
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
Set of objects whose state must satisfy limits
number of constraints or limitations. CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which
Constraint satisfaction problem
Constraint_satisfaction_problem
Problem in combinatorial optimization
The knapsack problem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items
Knapsack_problem
Problem of deciding whether an expression equals zero
constant problem is the problem of deciding whether a given expression is equal to zero. This problem is also referred to as the identity problem or the
Constant_problem
Mathematical description of quantum state
is reduced to a problem of lower dimensionality. The associated Laguerre polynomials appear in the hydrogenic wave function problem after factoring out
Wave_function
Approximating an arbitrary function with a well-behaved one
In general, a function approximation problem asks us to select a function that closely matches ("approximates") a function in a task-specific way.[better source needed]
Function_approximation
Differential calculus on function spaces
least/stationary action. Many important problems involve functions of several variables. Solutions of boundary value problems for the Laplace equation satisfy
Calculus_of_variations
Unsolved problem in computer science
Unsolved problem in computer science If the solution to a problem can be checked in polynomial time, must the problem be solvable in polynomial time? More
P_versus_NP_problem
Method to solve optimization problems
in the polytope where this function has the largest (or smallest) value if such a point exists. Linear programs are problems that can be expressed in standard
Linear_programming
NP-hard problem in combinatorial optimization
problem has been shown to be NP-hard (more precisely, it is complete for the complexity class FPNP; see function problem), and the decision problem version
Travelling_salesman_problem
Machine learning model training problem
x_{t}} is a function of h t {\displaystyle h_{t}} , as some x t = G ( h t ) {\displaystyle x_{t}=G(h_{t})} . The vanishing gradient problem already presents
Vanishing_gradient_problem
Type of problem involving ODEs or PDEs
boundary value problems to be studied is the Dirichlet problem, of finding the harmonic functions (solutions to Laplace's equation); the solution was given
Boundary_value_problem
Type of computational problem
to the problem instance. Let c R ( x ) = | { y ∣ R ( x , y ) } | {\textstyle c_{R}(x)=\vert \{y\mid R(x,y)\}\vert \,} be the counting function. That is
Counting_problem_(complexity)
Complexity class used to classify decision problems
solutions for NP-complete problems, then NP = RP and PH ⊆ BPP. NP is a class of decision problems; the analogous class of function problems is FNP. The only known
NP_(complexity)
Subfield of mathematical optimization
optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many
Convex_optimization
Abstract machine used to study decision problems
entity capable of solving some problem, which for example may be a decision problem or a function problem. The problem does not have to be computable;
Oracle_machine
Problem in differential geometry
geometry, Bernstein's problem is as follows: if the graph of a function on Rn−1 is a minimal surface in Rn, does this imply that the function is linear? This
Bernstein's_problem
the perturbation function is any function which relates to primal and dual problems. The name comes from the fact that any such function defines a perturbation
Perturbation_function
the set of function problems that are solvable in polynomial time by a deterministic Turing machine with an oracle for some decision problem in NP. In
NP-easy
Problem of solving a partial differential equation subject to prescribed boundary values
In mathematics, a Dirichlet problem asks for a function which solves a specified partial differential equation (PDE) in the interior of a given region
Dirichlet_problem
Mathematical problem involving optimal stopping theory
known as the marriage problem, the sultan's dowry problem, the fussy suitor problem, the googol game, and the best choice problem. Its solution is also
Secretary_problem
Analytic function in mathematics
zeta function that many mathematicians consider the most important unsolved problem in pure mathematics. The values of the Riemann zeta function at even
Riemann_zeta_function
Probability of shared birthdays
hash function, as well as calculating the approximate risk of a hash collision existing within the hashes of a given size of population. The problem is
Birthday_problem
Computer software bug occurring in 2038
The year 2038 problem (also known as Y2038, Y2K38, Y2K38 superbug, or the Epochalypse) is a time computing problem that leaves some computer systems unable
Year_2038_problem
follow from the well-known total function problem (Does a given machine halt for every input?), since the latter problem concerns only valid computations
Mortality (computability theory)
Mortality_(computability_theory)
exponential function problem concerns the extension of this theory to another primitive operation, the exponential function. It is an open problem whether
Decidability of first-order theories of the real numbers
Decidability_of_first-order_theories_of_the_real_numbers
Major unsolved problem in transcendental number theory
+ mnxn = 0. This would be a positive solution to Tarski's exponential function problem. A related conjecture called the uniform real Schanuel's conjecture
Schanuel's_conjecture
Problem-solving procedures with certain characteristics
for solving a problem from a specific class. An effective method is sometimes also called a mechanical method or procedure. Functions for which an effective
Effective_method
Yes-or-no question that cannot ever be solved by a computer
computable function that correctly answers every question in the problem set. The connection between these two is that if a decision problem is undecidable
Undecidable_problem
Special mathematical function defined as sin(x)/x
except at the point x = 0, and illustrates the problem of thinking of the delta function as a function rather than as a distribution. A similar situation
Sinc_function
hash functions can be divided into two main categories. In the first category are those functions whose designs are based on mathematical problems, and
Security of cryptographic hash functions
Security_of_cryptographic_hash_functions
Artificial neural network node function
activation function of a node is a function that calculates the output of the node based on its individual inputs and their weights. Nontrivial problems can
Activation_function
Conceptual conflict between general relativity and quantum mechanics
In theoretical physics, the problem of time is a conceptual conflict between quantum mechanics and general relativity. Quantum mechanics regards the flow
Problem_of_time
Function used as a performance test problem for optimization algorithms
In mathematical optimization, the Ackley function is a non-convex function used as a performance test problem for optimization algorithms. It was proposed
Ackley_function
Function that is continuous everywhere but differentiable nowhere
mathematics, the Weierstrass function, named after its discoverer, Karl Weierstrass, is an example of a real-valued function that is continuous everywhere
Weierstrass_function
Class of computational problems
Unbounded search operator Decision problem Optimization problem Counting problem (complexity) Function problem Search games Luca Trevisan (2010), Stanford
Search_problem
Whether a decision problem has an effective method to derive the answer
fields, established by Tarski in 1949 (see also Tarski's exponential function problem). The first-order theory of Euclidean geometry, established by Tarski
Decidability_(logic)
Mathematical concept
that is concerned with mathematical optimization problems involving more than one objective function to be optimized simultaneously. Multi-objective is
Multi-objective_optimization
Mathematical formula involving a given set of operations
the functions that have a closed form are called elementary functions. The closed-form problem arises when new ways are introduced for specifying mathematical
Closed-form_expression
Numerical method for solving physical or engineering problems
formulation of a boundary value problem finally results in a system of algebraic equations. The method approximates the unknown function over the domain. The simple
Finite_element_method
Generalized function whose value is zero everywhere except at zero
Dirac delta function (or δ {\displaystyle {\boldsymbol {\delta }}} distribution), also known as the unit impulse, is a generalized function on the real
Dirac_delta_function
18 mathematical problems stated in 1998
Smale's problems is a list of eighteen unsolved problems in mathematics proposed by Steve Smale in 1998 and republished in 1999. Smale composed this list
Smale's_problems
Solution process for some optimization problems
optimization problem where some of the constraints are not linear equalities or the objective function is not a linear function. An optimization problem is one
Nonlinear_programming
On the distribution of prime numbers
and is actually a set of three different problems: the original Riemann hypothesis for the Riemann zeta function the solvability of two-variable, linear
Hilbert's_eighth_problem
Type of calculus problem
value problem (IVP) is an ordinary differential equation together with an initial condition which specifies the value of the unknown function at a given
Initial_value_problem
Extension of the factorial function
number theory, and combinatorics. The gamma function can be seen as a solution to the interpolation problem of finding a smooth curve y = f ( x ) {\displaystyle
Gamma_function
Functions used to evaluate optimization algorithms
of problems. In the first part, some objective functions for single-objective optimization cases are presented. In the second part, test functions with
Test functions for optimization
Test_functions_for_optimization
problem in which the objective function and constraints are all differentiable functions. Using this concept a lower bound for a minimization problem
Wolfe_duality
Necessary condition for optimality associated with dynamic programming
written as a function of the state, is called the value function.[citation needed] Bellman showed that a dynamic optimization problem in discrete time
Bellman_equation
American mathematician and Nobel Laureate (1928–2015)
Schwartz, and Eduard Zehnder. Nash himself analyzed the problem in the context of analytic functions. Schwartz later commented that Nash's ideas were "not
John_Forbes_Nash_Jr.
Type of computational problem
Computational problem Decision problem Optimization problem Search problem Counting problem (complexity) Function problem TFNP "Promise problem". Complexity
Promise_problem
Study of computable functions and Turing degrees
open problems in this area. This branch of computability theory analyzed the following question: For fixed m and n with 0 < m < n, for which functions A
Computability_theory
Real function with secant line between points above the graph itself
number). Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they
Convex_function
the utility function and Marshallian demand in the utility maximization problem mirrors the relationship between the expenditure function and Hicksian
Expenditure minimization problem
Expenditure_minimization_problem
Quantum algorithm
computing software development framework by IBM. Hidden Linear Function problem Simon's problem Ethan Bernstein and Umesh Vazirani (1997). "Quantum Complexity
Bernstein–Vazirani_algorithm
Process by which a quantum system takes on a definitive state
interpretations of quantum mechanics, wave function collapse, also called reduction of the state vector, occurs when a wave function—initially in a superposition of
Wave_function_collapse
Summatory function of the divisor-counting function
zeta function. The various studies of the behaviour of the divisor function are sometimes called divisor problems. The divisor summatory function is defined
Divisor_summatory_function
Method for estimating new data within known data points
of that function for an intermediate value of the independent variable. A closely related problem is the approximation of a complicated function by a simple
Interpolation
2012 single by E-40 featuring YG, Iamsu! and Problem
Video: E-40 "Function" Feat. YG, Problem & IamSU!". YouTube. 2012-03-05. Retrieved 2016-07-25. "E-40 "Function" Ft. YG, IamSu, and Problem". YouTube. 2012-01-14
Function_(song)
One-way cryptographic tool
not a sturdy trapdoor function – modern computers can guess all of the possible answers within a second – but this sample problem could be improved by
Trapdoor_function
Maximized objective function of an optimization problem
The value function of an optimization problem gives the value attained by the objective function at a solution, while only depending on the parameters
Value_function
Measure of the shape of a function
Moments of a function in mathematics are certain quantitative measures related to the shape of the function's graph. For example, if the function represents
Moment_(mathematics)
approximate solutions to function problems, especially optimization problems. An FPTAS takes as input an instance of the problem and a parameter ε > 0.
Fully polynomial-time approximation scheme
Fully_polynomial-time_approximation_scheme
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