However, with only authoritative name servers operating, every DNS query must start with recursive queries at the root zone of the Domain Name System and each user system must implement resolver software capable of recursive operation.

A DNS query may be either a non-recursive query or a recursive query:

The resolver, or another DNS server acting recursively on behalf of the resolver, negotiates use of recursive service using bits in the query headers.

Caching name servers are often also recursive name servers — they perform every step necessary to answer any DNS query they receive.

SPARQL ( pronounced " sparkle ", a recursive acronym for SPARQL Protocol and RDF Query Language ) is an RDF query language, that is, a query language for databases, able to retrieve and manipulate data stored in Resource Description Framework format.

The set of equations ( 5 ), ( 6 ), and the starting equation ( 7 ) is of a recursive type well suited to programming on the digital computer.

Note that " completeness " has a different meaning here than it does in the context of Gödel's first incompleteness theorem, which states that no recursive, consistent set of non-logical axioms of the Theory of Arithmetic is complete, in the sense that there will always exist an arithmetic statement such that neither nor can be proved from the given set of axioms.

In computability theory, the Ackermann function, named after Wilhelm Ackermann, is one of the simplest and earliest-discovered examples of a total computable function that is not primitive recursive.

However, the recursion is bounded because in each recursive application either m decreases, or m remains the same and n decreases.

If we define the function f ( n ) = A ( n, n ), which increases both m and n at the same time, we have a function of one variable that dwarfs every primitive recursive function, including very fast-growing functions such as the exponential function, the factorial function, multi-and superfactorial functions, and even functions defined using Knuth's up-arrow notation ( except when the indexed up-arrow is used ).

This extreme growth can be exploited to show that f, which is obviously computable on a machine with infinite memory such as a Turing machine and so is a computable function, grows faster than any primitive recursive function and is therefore not primitive recursive.

Seed AI is a hypothesized type of strong artificial intelligence capable of recursive self-improvement.

A common adaptive method is recursive subdivision, in which a curve's control points are checked to see if the curve approximates a line segment to within a small tolerance.

The recursive equation is best introduced in a slightly more general form

Although the above recursive formula can be used for computation it is

It is not feasible to carry out such a computation using the above recursive formulae, since at least ( a constant multiple of ) p < sup > 2 </ sup > arithmetic operations would be required.

Note that this is different from the recursive languages which can be decided by an always-halting Turing machine.

Note that the set of grammars corresponding to recursive languages is not a member of this hierarchy.

Every regular language is context-free, every context-free language, not containing the empty string, is context-sensitive and every context-sensitive language is recursive and every recursive language is recursively enumerable.

A recursive definition, sometimes also called an inductive definition, is one that defines a word in terms of itself, so to speak, albeit in a useful way.

Using the following observation, one can create a recursive algorithm that computes x < sup > n </ sup > for an integer n using squaring and multiplication:

As one illustration, trees, ferns, cells of the nervous system, blood and lung vasculature, and other branching patterns in nature can be modeled on a computer by using recursive algorithms and L-systems techniques.

A recursive pun is one in which the second aspect of a pun relies on the understanding of an element in the first.

⟨ X | R ⟩ of a group H, one can recursively enumerate all homomorphisms h: H → G by first enumerating all mappings h < sup >†</ sup >: X → G. Not all of these mappings extend to homomorphisms, but, since h < sup >†</ sup >( R ), is finite, it is possible to distinguish between homomorphism and non-homomorphisms by using the solution to the word problem in G. " Weeding out " non-homomorphisms gives the required recursive enumeration: h < sub > 1 </ sub >, h < sub > 2 </ sub >, ..., h < sub > n </ sub >, ....

Act II opens with Vladimir singing a recursive round about a dog, which could illustrate the cyclical nature of the play's universe, and also point toward the play's debt to the carnivalesque, music hall traditions, and vaudeville comedy ( this is only one of a number of canine references and allusions in the play ).

Identificazione di una donna ( Identification of a Woman, 1982 ), filmed in Italy, deals one more time with the recursive subjects of his Italian trilogy.

Here's an example of a recursive one:

It is an open question to give supports for a Church thesis for fuzzy mathematics the proposed notion of recursive enumerability for fuzzy subsets is the adequate one.

The list of moves for a tower being carried from one peg onto another one, as produced by the recursive algorithm has many regularities.

In computer science, a recursive descent parser is a kind of top-down parser built from a set of mutually recursive procedures ( or a non-recursive equivalent ) where each such procedure usually implements one of the production rules of the grammar.

Systems explored in the book include cellular automata in one, two, and three dimensions ; mobile automata ; Turing machines in 1 and 2 dimensions ; several varieties of substitution and network systems ; primitive recursive functions ; nested recursive functions ; combinators ; tag systems ; register machines ; reversal-addition ; and a number of other systems.

This usage may seem odd, but it is possible to prove that if a group has a presentation with recursively enumerable then it has another one with recursive.

Hence, one can easily formulate the solution for finding shortest paths in a recursive manner, which is what the Bellman-Ford algorithm or the Floyd-Warshall algorithm does.

This identity is quite useful in conjunction with the recursive generating formula, inasmuch as it enables one to calculate the cosine of any integral multiple of an angle solely in terms of the cosine of the base angle.

In other words X is if it is defined by a formula allowed to ask questions about membership in Y. Alternatively one can view the sets as those sets that can be built starting with sets recursive in Y and alternatively projecting and taking the complements of these sets up to n times.

In recursive implementations of D & C algorithms, one must make sure that there is sufficient memory allocated for the recursion stack, otherwise the execution may fail because of stack overflow.

As one of the examples used to demonstrate such reasoning, Manna's book includes a non-recursive algorithm that simulates the original ( recursive ) 91 function.

A formal derivation of the non-recursive version from the recursive one was given in a 1980 article by Mitchell Wand, based on the use of continuations.

A variant of the AA compiler included run-time support for a top-down recursive descent parser.

A recursive definition for the Bézier curve of degree n expresses it as a point-to-point linear combination of a pair of corresponding points in two Bézier curves of degree n − 1.

One has a recursive formula for binomial coefficients

Bernard Baars proposed that once in place, this " recursive " circuitry may have provided a basis for the subsequent development of many of the functions that consciousness facilitates in higher organisms.

The combination of DNS caching and recursive functions in a name server is not mandatory ; the functions can be implemented independently in servers for special purposes.

Internet service providers typically provide recursive and caching name servers for their customers.

These simple resolvers ( called " stub resolvers ") rely on a recursive name server to perform the work of finding information for them.

This formula is used for recursive generation of cos ( nx ) for integer values of n and arbitrary x ( in radians ).

:* Simple and " perhaps recursive " definitions see Common techniques for generating fractals

A theory about some topic is usually first-order logic together with: a specified domain of discourse over which the quantified variables range, finitely many functions which map from that domain into it, finitely many predicates defined on that domain, and a recursive set of axioms which are believed to hold for those things.

Most programming environments with recursive subroutines use a stack for control flow.

One implicitly stack-based ( recursive ) flood-fill implementation ( for a two-dimensional array ) goes as follows:

It is similar to the simple recursive solution, except that instead of making recursive calls, it pushes the nodes into a LIFO queue — acting as a stack — for consumption:

* Sample implementations for recursive and non-recursive, classic and scanline flood fill, by Lode Vandevenne.

HURD is a mutually recursive acronym, standing for HIRD of Unix-replacing daemons, where HIRD stands for HURD of interfaces representing depth.

The more famous incompleteness theorem states that for any self-consistent recursive axiomatic system powerful enough to describe the arithmetic of the natural numbers ( for example Peano arithmetic ), there are true propositions about the naturals that cannot be proved from the axioms.

The name LAME is a recursive acronym for " LAME Ain't an MP3 Encoder ".

Each frame is both a generic component in a hierarchy of nested subassemblies, and a procedure for integrating itself with its subassembly frames ( a recursive process that resolves integration conflicts in favor of higher level subassemblies ).