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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
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
Seven mathematical problems with a US$1 million prize for each solution
Millennium Prize Problems are seven well-known complex mathematical problems selected by the Clay Mathematics Institute in 2000. Each of the problems has a prize
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
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
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
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
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
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
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
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
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)
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
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
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
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
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
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
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
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
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
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)
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
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
Millennium Prize Problem
smoothness problem, the external force f ( x , t ) {\displaystyle \mathbf {f} (x,t)} is assumed to be a smooth function, a real analytic function, or equal
Navier–Stokes existence and smoothness
Navier–Stokes_existence_and_smoothness
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
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
generalizations for different types of L-functions that are expected to be true. The Millennium Prize problem is offered for showing the original Riemann
List of unsolved problems in mathematics
List_of_unsolved_problems_in_mathematics
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)
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
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
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
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
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
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
Unsolved problem in computer science
Unsolved problem in computer science If the solution to a problem can be verified in polynomial time, must the problem be solvable in polynomial time
P_versus_NP_problem
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
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
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
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
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
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
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
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
Class of computational problems
Unbounded search operator Decision problem Optimization problem Counting problem (complexity) Function problem Search games Luca Trevisan (2010), Stanford
Search_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
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
of complex systems, a function tree is a diagram showing the dependencies between the functions of a system. It breaks a problem (or its solution) down
Function_tree
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
2012 single by E-40 featuring YG, Iamsu! and Problem
Video: E-40 "Function" Feat. YG, Problem & IamSU!". YouTube. March 5, 2012. Retrieved July 25, 2016. "E-40 "Function" Ft. YG, IamSu, and Problem". YouTube
Function_(song)
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
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
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
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
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
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
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
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
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
Complexity class
complexity theory, the complexity class FNP is the function problem extension of the decision problem class NP. The name is somewhat of a misnomer, since
FNP_(complexity)
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
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
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
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
Field of machine learning
are noisy, though this problem is mitigated to some extent by temporal difference methods. Using the so-called compatible function approximation method
Reinforcement_learning
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)
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
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
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
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
Measure of the shape of a function
moment problem). The same is not true on unbounded intervals (Hamburger moment problem). The nth moment of a real-valued continuous density function f (
Moment_(mathematics)
Continuous function whose value increases to infinity
of an optimization problem. Such functions are used to replace inequality constraints by a penalizing term in the objective function that is easier to
Barrier_function
23 mathematical problems stated in 1900
of the functions defining the group Mathematical treatment of the axioms of physics Irrationality and transcendence of certain numbers Problems of prime
Hilbert's_problems
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
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)
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)
Probabilistic optimization technique and metaheuristic
a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. For large
Simulated_annealing
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
problem in which the objective function and constraints are all differentiable functions. Using this concept a lower bound for a minimization problem
Wolfe_duality
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
Concept in convex analysis
this, if the function's domain is empty or if the function is identically equal to + ∞ {\displaystyle +\infty } then the minimization problem once again
Proper_convex_function
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)
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
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
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
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
Group theory function
complexity of the word problem in groups. In particular, a finitely presented group has solvable word problem if and only if the Dehn function for a finite presentation
Dehn_function
Problem of allocation of money by consumers in order to most benefit themselves
the utility function and Marshallian demand in the utility maximization problem mirrors the relationship between the expenditure function and Hicksian
Utility_maximization_problem
Mathematical function
\sin } . The Jacobi elliptic functions are used more often in practical problems than the Weierstrass elliptic functions as they do not require notions
Jacobi_elliptic_functions
Sequence of program instructions invokable by other software
In computer programming, a function (also procedure, method, subroutine, routine, or subprogram) is a callable unit of software logic that has a well-formed
Function (computer programming)
Function_(computer_programming)
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
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
Type of algorithm for constrained optimization
original constrained problem. The unconstrained problems are formed by adding a term, called a penalty function, to the objective function that consists of
Penalty_method
Function used as a performance test problem for optimization algorithms
Rastrigin function of two variables In mathematical optimization, the Rastrigin function is a non-convex function used as a performance test problem for optimization
Rastrigin_function
Formal power series
generating function, if any, that is most useful in a given context will depend upon the nature of the sequence and the details of the problem being addressed
Generating_function
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)
On solutions of 7th-degree equations
originally posed his problem for algebraic functions ("...Existenz von algebraischen Funktionen...", i.e., "...existence of algebraic functions..."; also see
Hilbert's_thirteenth_problem
Concept in mathematical optimization
approach, the constrained maximization (minimization) problem is rewritten as a Lagrange function whose optimal point is a global maximum or minimum over
Karush–Kuhn–Tucker_conditions
travel, tourism, insurance
FUNCTION PROBLEM
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FUNCTION PROBLEM
travel, tourism, insurance