Informally, it asks whether every problem whose solution can be quickly verified by a computer can also be quickly solved by a computer.

Informally, the " P vs. NP " question asks whether every optimization problem whose answers can be efficiently verified for correctness / optimality can be solved optimally with an efficient algorithm.

Informally it solves the following problem: Given an integer N, find its prime factors.

" Informally, hypothesis boosting problem asks whether an efficient learning algorithm that outputs an hypothesis whose performance is only slightly better than random guessing a weak learner implies the existence of an efficient algorithm that outputs an hypothesis of arbitrary accuracy a strong learner.

Informally, given a problem, the Turing jump returns the set of Turing machines which halt when given access to an oracle that solves that problem.

Informally, the Fatou set of the function consists of values with the property that all nearby values behave similarly under repeated iteration of the function, and the Julia set consists of values such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values.

Informally, a thick object in our space is simply connected if it consists of one piece and does not have any " holes " that pass all the way through it.

Informally: a formula in prenex form containing existential quantifiers only is provable ( valid ) in first-order logic if and only if a disjunction composed of substitution instances of the quantifier-free subformula of is a tautology ( propositionally derivable ).

Informally, we can consider these products on the left hand side as being elements of the free group F =

Informally, these theorems say that given more time, a Turing machine can solve more problems.

Informally, these conditions state that the dual of a statement is formed by reversing arrows and compositions.

Informally, to estimate the area of a domain D, first pick a simple domain E whose area is easily calculated and which contains D. Now pick a sequence of random points that fall within E. Some fraction of these points will also fall within D. The area of D is then estimated as this fraction multiplied by the area of E.

Informally put, the axiom of choice says that given any collection of bins, each containing at least one object, it is possible to make a selection of exactly one object from each bin.

Informally, it is a permutation of the group elements such that the structure remains unchanged.

Informally known as " The Big Book " ( with its first 164 pages virtually unchanged since the 1939 edition ), it suggests a twelve-step program in which members admit that they are powerless over alcohol and need help from a " higher power "; seek guidance and strength through prayer and meditation from God or Higher Power of their own understanding ; take a moral inventory with care to include resentments ; list and become ready to remove character defects ; list and make amends to those harmed, and then try to help other alcoholics recover.

Informally, it is the similarity between observations as a function of the time separation between them.

Informally, this is true because polynomial time algorithms are closed under composition.

Informally basis vectors are like " building blocks of a vector ", they are added together to make a vector, and the coordinates are the number of basis vectors in each direction.

Informally, the theorem says that the curvature of a surface can be determined entirely by measuring angles and distances on the surface.

Informally, w represents a " script " for the computable function f, and F represents an " interpreter " that parses the script as a prefix of its input and then executes it on the remainder of input.

Such a definition can be formulated in terms of equivalence classes of smooth functions on M. Informally, we will say that two smooth functions f and g are equivalent at a point x if they have the same first-order behavior near x.

Informally, an object is reachable if it is referenced by at least one variable in the program, either directly or through references from other reachable objects.

Informally, a relational database table is often described as " normalized " if it is in the Third Normal Form.

Informally, a graph is a good expander if it has low degree and high expansion parameters.

( Informally, input positions can be thought of as locations at token boundaries.

* Informally known as FORTRAN 66.

* Informally known as Fortran 90.

* Informally known as Fortran 95.

* Informally known as Fortran 2003.

* Informally known as Fortran 2008.

Informally, the expression " infinitesimal calculus " became commonly used to refer to Weierstrass ' approach but has become something of a dead metaphor.

Informally, Kajang is known as the " Satay Town ", and is famous among tourists and locals alike.

Informally we can think of elements of the Lie algebra as elements of the group that are " infinitesimally close " to the identity, and the Lie bracket is something to do with the commutator of two such infinitesimal elements.

Informally, a measure has the property of being monotone function | monotone in the sense that if A is a subset of B, the measure of A is less than or equal to the measure of B.

Algorithm analysis is an important part of a broader computational complexity theory, which provides theoretical estimates for the resources needed by any algorithm which solves a given computational problem.

In the field of artificial intelligence, the most difficult problems are informally known as AI-complete or AI-hard, implying that the difficulty of these computational problems is equivalent to solving the central artificial intelligence problem — making computers as intelligent as people, or strong AI.

It is a challenge to functionalism and the computational theory of mind, and is related to such questions as the mind-body problem, the problem of other minds, the symbol-grounding problem, and the hard problem of consciousness.

* Collision detection, the computational problem of detecting the intersection of two or more objects

In this context, a computational problem is understood to be a task that is in principle amenable to being solved by a computer ( i. e. the problem can be stated by a set of mathematical instructions ).

A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem.

A computational problem can be viewed as an infinite collection of instances together with a solution for every instance.

The input string for a computational problem is referred to as a problem instance, and should not be confused with the problem itself.

In computational complexity theory, a problem refers to the abstract question to be solved.

For this reason, complexity theory addresses computational problems and not particular problem instances.

When considering computational problems, a problem instance is a string over an alphabet.

In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer, depending on the values of some input parameters.

" Difficult ", in this sense, is described in terms of the computational resources needed by the most efficient algorithm for a certain problem.

A distributed system may have a common goal, such as solving a large computational problem.