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

Informally, a computational problem consists of problem instances and solutions to these problem instances.

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, 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, a set of natural numbers A is Turing reducible to a set B if there is an oracle machine that correctly tells whether numbers are in A when run with B as the oracle set ( in this case, the set A is also said to be ( relatively ) computable from B and recursive in B ).

Informally, the second axiom says it doesn't matter whether we restrict to W in one step or restrict first to V, then to W.

Informally the Church – Turing thesis states that if some method ( algorithm ) exists to carry out a calculation, then the same calculation can also be carried out by a Turing machine ( as well as by a recursively definable function, and by a λ-function ).

In other words, L can be solved in polynomial time by an oracle machine with an oracle for H. Informally, we can think of an algorithm that can call such an oracle machine as a subroutine for solving H, and solves L in polynomial time, if the subroutine call takes only one step to compute.

Informally, this means that given a constructive proof that an object exists, then that constructive proof can be turned into an algorithm for generating an example of it.

Informally, the algorithm constructs a finite state machine that resembles a trie with additional links between the various internal nodes.

Informally, this is true because a polynomial-time algorithm can make polynomially many queries to other polynomial-time algorithms, retaining its polynomial running time.

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, a superkey is a set of attributes within a table whose values can be used to uniquely identify a tuple.

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, 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, 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, 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.

Informally, word formation rules form " new words " ( that is, new lexemes ), while inflection rules yield variant forms of the " same " word ( lexeme ).

Informally speaking, the prime number theorem states that if a random integer is selected in the range of zero to some large integer N, the probability that the selected integer is prime is about 1 / ln ( N ), where ln ( N ) is the natural logarithm of N. For example, among the positive integers up to and including N = 10 < sup > 3 </ sup > about one in seven numbers is prime, whereas up to and including N = 10 < sup > 10 </ sup > about one in 23 numbers is prime ( where ln ( 10 < sup > 3 </ sup >)= 6. 90775528. and ln ( 10 < sup > 10 </ sup >)= 23. 0258509 ).

Informally, he may have been known as " Dickon ", according to a sixteenth-century legend of a note, warning of treachery, that was sent to the Duke of Norfolk on the eve of Bosworth: " Jack of Norffolke be not to bolde ,/ For Dyckon thy maister is bought and solde ".

Informally the word is also used to describe a procedure or process with a specific purpose.

Informally, a permutation of a set of objects is an arrangement of those objects into a particular order.

Informally, a set of strategies is a Nash equilibrium if no player can do better by unilaterally changing his or her strategy.

Informally, two sequences ( a < sub > n </ sub >) and ( b < sub > n </ sub >) become closer and closer if and only if more and more of their terms agree exactly.

Informally, G has the above presentation if it is the " freest group " generated by S subject only to the relations R. Formally, the group G is said to have the above presentation if it is isomorphic to the quotient of a free group on S by the normal subgroup generated by the relations R.

Informally speaking, a step function is a piecewise constant function having only finitely many pieces.

Informally known as LaGuardia Arts, or LaGuardia High School, Fiorello H. LaGuardia High School of Music & Art and Performing Arts is the only school among the nine specialized high schools in New York City that receives special funding from the New York State legislature through the Hecht Calandra Act.

Informally, a skein relation gives a linear relation between the values of a knot polynomial on a collection of three links which differ from each other only in a small region.

Informally, a free object over a set A can be thought as being a " generic " algebraic structure over A: the only equations that hold between elements of the free object are those that follow from the defining axioms of the algebraic structure.

Informally, this reads as follows: something exists with the property F, there is only one such thing, and this unique thing also has the property G.

Informally, in attempting to estimate the causal effect of some variable x on another y, an instrument is a third variable z which affects y only through its effect on x.

Informally, lowness means that problems in B are not only solvable by machines which can solve problems in A, but are " easy to solve.

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 ).

A pure or homogeneous simplicial k-complex is a simplicial complex where every simplex of dimension less than k is a face of some simplex of dimension exactly k. Informally, a pure 1-complex " looks " like it's made of a bunch of lines, a 2-complex " looks " like it's made of a bunch of triangles, etc.

Informally, subvarieties are in general position if they cannot be described more simply than others.