The primitiverecursive functions are defined using primitive Recursion computer science recursion and function ... recursive, although some are known see the section on Primitiverecursivefunction Limitations ... complexity theory complexity theory . Every primitiverecursivefunction is a general recursivefunction. Definition The primitiverecursive functions are among the number theoretic functions ... primitiverecursive functions are given by these axiom s Constant function The 0 ary constant term constant function 0 is primitiverecursive. Successor function The 1 ary successor function S , which ... Composition Given f , a k ary primitiverecursivefunction, and k m ary primitiverecursive ... function, and g , a k 2 ary primitiverecursivefunction, the k 1 ary function h is defined as the primitive recursion of f and g , i.e. the function h is primitiverecursive when math h 0, x 1, ldots ... recursivefunction is a partial recursivefunction that is defined for every input. Every primitiverecursivefunction is total recursive, but not all total recursive functions are primitiverecursive. The Ackermann function A m , n is a well known example of a total recursivefunction that is not primitive ... is primitiverecursive if and only if there is a natural number m such that the function can ... of the arguments of the primitiverecursivefunction. Citation needed date February 2007 An important ... computable function f e , n such that For every primitiverecursivefunction g ... set of total computable functions. Limitations This section is linked from Primitiverecursivefunction ... provides a total computable function that is not primitiverecursive. A sketch of the proof ... infinitely many definitions of any one primitiverecursivefunction . This means that the mvar n th definition of a primitiverecursivefunction in this enumeration can be effectively determined ... n th definition in the list is computed by a primitiverecursivefunction of mvar n . Let math f ... more details
Recursivefunction may refer to Recursion computer science , a procedure or subroutine, implemented in a programming language, whose implementation references itself A total computable function , a function which is defined for all possible inputs See also recursivefunction , defined from a particular formal model of computable functions using primitive recursion and the operator Recurrence relation , in mathematics, an equation that defines a sequence recursively disambig Category Recursion cs Rekurzivn funkce ru ... more details
propositions involving natural number s and any primitiverecursivefunction , including the operations ... connectives The equality symbol , the constant symbol 0 , and the primitiverecursivefunction successor symbol S meaning add one A symbol for each primitiverecursivefunction . The logical axioms ... 0 math math S x S y to x y, math and recursive defining equations for every primitiverecursivefunction ... arithmetic , the only primitiverecursivefunction s that need to be explicitly axiomatized are addition and multiplication . All other primitiverecursive predicates can be defined using these two primitiverecursive functions and quantification over all natural numbers . Defining primitiverecursivefunction s in this manner is not possible in PRA, because it lacks quantifier s. Logic free calculus ... . Negation can be expressed as math 1 dot x y 0 math . See also Elementary recursive arithmetic Heyting arithmetic Peano arithmetic Second order arithmetic primitiverecursivefunction References references ...Primitiverecursive arithmetic , or PRA , is a quantifier free formalization of the natural numbers . It was first ... of PRA is just an equation between two terms. In this setting a term is a primitiverecursivefunction of zero or more variables. In 1941 Haskell Curry gave the first such system ref Haskell Curry , http www.jstor.org stable 2371522 A Formalization of Recursive Arithmetic . American Journal of Mathematics ..., and F , G , and H are any primitiverecursive functions which may have parameters other than the ones ... are any terms primitiverecursive functions of zero or more variables . Finally, there are symbols for any primitiverecursive functions with corresponding defining equations, as in Skolem s system ... can be extended to forms of recursion beyond primitive recursion, up to epsilon 0 &epsilon sub ... resolveppn GDZPPN002343355 Logic free formalisations of recursive arithmetic , Mathematica Scandinavica ... can be defined by primitive recursion math begin align P 0 0 quad & quad P S x x x dot 0 x quad & quad ... more details
In mathematical logic , the primitiverecursive functionals are a generalization of primitiverecursive functions into higher type theory . They consist of a collection of functions in all pure finite types. The primitiverecursive functionals are important in proof theory and constructive mathematics They are a central part of the Dialectica interpretation of intuitionistic arithmetic developed by Kurt G del . In recursion theory , the primitiverecursive functionals are an example of higher type computability, as primitiverecursive functions are examples of Turing computability. Background Every primitiverecursive functional has a type, which tells what kind of inputs it takes and what kind of output it produces. An object of type 0 is simply a natural number it can also be viewed as a constant function that takes no input and returns an output in the set N of natural numbers. For any two types &sigma and &tau , the type &sigma &rarr &tau represents a function that takes an input of type &sigma and returns an output of type &tau . Thus the function f n n 1 is of type 0&rarr 0. The types 0&rarr 0 &rarr 0 and 0&rarr 0&rarr 0 are different by convention, the notation 0&rarr 0&rarr ... The primitiverecursive functionals are the smallest collection of objects of finite type such that The constant function f n 0 is a primitiverecursive functional The successor function g n n 1 is a primitiverecursive functional For any type &sigma &tau , the functional K x sup &sigma sup , y sup &tau sup x is a primitiverecursive functional For any types &rho , &sigma , &tau , the functional S r sup &rho &rarr &sigma &rarr &tau sup , s sup &rho &rarr &sigma sup , t sup &rho sup r t s t is a primitiverecursive functional For any type &tau , and f of type &tau , and any g of type 0&rarr ... f , g n 1 g n , R f , g n is a primitiverecursive functional References cite book title G del s functional ... as inputs a function f from N to N , and a natural number n , and returns f n . Then A has type 0 ... more details
Non recursivefunction might refer to Recursion computer science a procedure or subroutine, implemented in a programming language, whose implementation references itself recursivefunction , defined from a particular formal model of computable functions using primitive recursion and the operator Computable function , or total recursivefunction, a function computable by a turing machine Turing machine See also Recursivefunction disambig cs Rekurzivn funkce ... more details
recursion i.e. without minimisation is the class of primitiverecursive functions . While all primitiverecursive functions are total, this is not true of partial recursive functions for example, the minimisation of the successor function is undefined. The set of total recursive functions is a subset of the partial recursive functions and is a superset of the primitiverecursive functions functions like the Ackermann function can be proven to be total recursive, and not primitive. The first ... number for the function f . A consequence of this result is that any recursivefunction can be defined using a single instance of the operator applied to a total primitiverecursivefunction. Minsky ...lowercase title recursivefunction In mathematical logic and computer science , the recursive functions are a class of partial function s from natural number s to natural number s which are computable ... k , math . Primitive recursion operator math rho , math Given the k ary function math g x 1, ldots ... in the corresponding partial recursivefunction. The unbounded search operator is not definable ... recursivefunction math f x 1, ldots,x k math with k free variables there is an e such that math ... the definition of a general recursivefunction U n, x that correctly interprets the number n and computes ... 13 Successor function Kleene uses x and S for Successor . As successor is considered to be primitive ... that the recursive functions are precisely the functions that can be computed by Turing machine s. The recursive functions are closely related to primitiverecursivefunction s, and their inductive definition below builds upon that of the primitiverecursive functions. However, not every recursivefunction is a primitiverecursivefunction &mdash the most famous example is the Ackermann function . Other equivalent classes of functions are the lambda recursivefunction &lambda recursive functions and the functions that can be computed by Markov algorithm s. The set of all recursive functions ... more details
wiktionary primitivePrimitive may refer to Anarcho primitivism , an anarchist critique of the origins and progress of civilization Primitive culture , one that lacks major signs of economic development or modernity Noble savage , uncorrupted by the influences of civilization Primitive communism , a pre agrarian form of communism according to Karl Marx and Friedrich Engels Primitive Church, another name for early Christianity Primitive Baptist , a religious movement seeking to retain or restore early Christian practices Primitive phylogenetics characteristic of an early stage of development or evolution, cf. Basal phylogenetics basal Meteorology Primitive equations , a set of nonlinear differential equations that are used to approximate atmospheric flow Mathematics Simple extension Primitive element field theory Primitive element finite field Primitive cell crystallography Primitive notion , axiomatic systems Primitive polynomial , one of two concepts Primitivefunction or Antiderivative , F &prime f Primitive group Primitive permutation group Primitive root of unity see Root of unity Definition . Computer science Language primitive , the simplest element provided by a programming language Machine code , instructions and data directly understandable by a CPU Primitive data type , a datatype provided by a programming language Geometric primitive , the simplest kinds of figures in computer graphics Cryptographic primitive s, low level cryptographic algorithms frequently used to build ... 20th century art movement Literature Primitive , a novel by J. F. Gonzalez Primitive , a novel by Mark Nykanen Music Primitive Cyndi Lauper song , by Cyndi Lauper Primitive The Groupies song , by The Groupies and covered by The Cramps The Primitives , a British indie rock band Primitive album , by Soulfly Primitive Neil Diamond album , by Neil Diamond Primitive Radio Gods , an American alternative rock band Primitive , a song by Annie Lennox, from her album Diva Annie Lennox album Diva album ... more details
recursive if there exists a total function total computable function math f such that math ... S var . In other words, the set math var S var is recursive if and only if the indicator function math 1 sub var S var sub is computable function computable . Examples Every finite or cofinite subset ...In computability theory , a Set mathematics set of natural number s is called recursive , computable or decidable if there is an algorithm which terminates after a finite amount of time and correctly decides whether or not a given number belongs to the set. A more general class of sets consists of the recursively enumerable set s, also called semidecidable sets. For these sets, it is only required that there is an algorithm that correctly decides when a number is in the set the algorithm may give .... A recursive language is a recursive subset of a formal language . The set of G del numbers ... Mathematica and related systems I see G del s incompleteness theorems . Properties If A is a recursive set then the complement set theory complement of A is a recursive set. If A and B are recursive sets then A B , A B and the image of A × B under the Cantor pairing function are recursive sets. A set A is a recursive set if and only if A and the complement set theory complement of A are both recursively enumerable set s. The preimage of a recursive set under a total function total computable function is a recursive set. The image of a computable set under a total computable bijection is computable. A set is recursive if and only if it is at level math &Delta su p 0 b 1 of the arithmetical hierarchy . A set is recursive if and only if it is either the range of a nondecreasing total computable function or the empty set. The image of a computable set under a nondecreasing total computable function is computable. References Cutland, N. Computability. Cambridge University Press, Cambridge New York, 1980. ISBN 0 521 22384 9 ISBN 0 521 29465 7 Rogers, H. The Theory of Recursive ... more details
Orphan date February 2009 Cleanup date February 2008 Recursive economics is a branch of modern economics based on highly complex mathematical function . The mathematical model model s are based on dynamical system dynamic differential equation s. This approach has been popularised by Robert Lucas, Jr. and Edward Prescott . Books Recursive Methods in Economic Dynamics by Nancy L. Stokey, Robert E. Lucas, Jr., Edward C. Prescott, Harvard 1989 economics stub Category Mathematical economics ... more details
In graph theory , a discipline within mathematics, a recursive tree i.e., unordered tree is a non planar labeled rooted tree graph theory tree . A size n recursive tree is labeled by distinct integers 1, 2, ..., n , where the labels are strictly increasing starting at the root labeled 1. Recursive trees are non planar, which means that the children of a particular node are not ordered. E.g. the following two size three recursive trees are the same. pre 1 1 2 3 3 2 pre Recursive trees also appear in the literature under the name Increasing Cayley trees. Properties The number of size n recursive trees is given by math T n n 1 . , math Hence the exponential generating function T z of the sequence T sub n sub is given by math T z sum n ge 1 T n frac z n n log left frac 1 1 z right . math Combinatorically a recursive tree can be interpreted as a root followed by an unordered sequence of recursive trees. Let F denote the family of recursive trees. math F circ frac 1 1 cdot circ times F frac 1 2 cdot circ times F F frac 1 3 cdot circ times F F F cdots circ times exp F , math where math circ math denotes the node labeled by 1, × the Cartesian product and math math the partition product for labeled objects. By translation of the formal description one obtains the differential equation for T z math T z exp T z , math with T 0 0. Bijections There are bijection bijective correspondences between recursive trees of size n and permutation s of size n &minus 1. Applications Recursive trees can be generated using a simple stochastic process. Such random recursive trees are used as simple models for epidemics. References Analytic Combinatorics , Philippe Flajolet and Robert Sedgewick, Cambridge University Press, 2008 Varieties of Increasing Trees , Francois ... of random recursive trees and binary search trees Michael Drmota and Hsien Kuei Hwang, Adv. Appl. Prob., 37, 1 21, 2005. Profiles of random trees Limit theorems for random recursive trees and binary ... more details
Chomsky 1959 . All recursive languages are also recursively enumerable language recursively enumerable ... context sensitive languages are recursive. Definitions There are two equivalent major definitions for the concept of a recursive language A recursive formal language is a recursive set recursive subset ... . A recursive language is a formal language for which there exists a Turing machine which will, when ... halts decider and is said to decide the recursive language. By the second definition, any ... inputs. An undecidable problem is a problem that is not decidable. Closure properties Recursive ... recursive languages, then the following languages are recursive as well The Kleene star math L math ... more details
case, and define the value of a function in terms of that value itself, rather than on other values of the function. Such a situation would lead to an infinite regress . Examples of recursive definitions ... that follows the recursive definition. For example, the definition of the natural numbers presented ... holds of all natural numbers Aczel 1978 742 . Form of recursive definitions Most recursive definition ... between a circular definition and a recursive definition is that a recursive definition must ... that recursive definitions are found. For example, a well formed formula wff can be defined as a symbol ... and Mary likes music. The value of such a recursive definition is that it can be used to determine ... a wff. KNpNq is K followed by Np and Nq and Np is a wff, etc. See also Recursive data type s Recursion ... , Discrete Structures, Logic, and Computability . ISBN 0 763 77206 2 DEFAULTSORT Recursive Definition ... more details
citations missing article date March 2007 Recursive Recycling is a technique where a function, in order to accomplish a task, calls itself with some part of the task or output from a previous step. In municipal solid waste and waste reclamation processing it is the process of extracting and converting materials from recycled materials derived from the previous step until all subsequent levels of output are extracted or used. Example Level 1 Recursive Solid waste or municipal solid waste can be treated, sanitized and separated under steam in a pressure vessel waste autoclave . Following the processing under steam and removal of toxic materials via condensate filtering, usable recyclables are immediately extracted for reuse plastics, ferrous metals, aluminum , glass, wood, etc. . Level 2 Recursive Organic material s from the original waste stream are converted to a fiber using steam at 60 psi and 160 C. The converted organics sanitary fiber is size reduced by 85 and can be used to produce bio fuels using acidic hydrolysis or enzymatic hydrolysis as Ethanol or may be used as Refuse Derived Fuel RDF . Level 3 Recursive After the monosacrides are extracted for distillation , the remaining residue used fiber can be used as a feed stock for electricity production. Level 4 Recursive Finally, the non toxic ash from the combusted fiber can be collected and used as a filler for preparation in super concrete and then reused in combination with similar materials gravel, stones, pottery, glass to form aggregate for construction materials. In true recursive recycling and conservation processing ... delivery of the derivatives. Analyst Commentary The concept of Recursive Recycling has been ... release. Since that pilot commercial facility stopped operating, the concept of Recursive Recycling ... of technologies to achieve full recursive levels has not been accepted. A number of companies ... wtd 679004 679032 679093 ?lang e RecyclingByMaterial DEFAULTSORT Recursive Recycling Category ... more details
In mathematics , specifically set theory , an ordinal number ordinal math alpha math is said to be recursive if there is a recursive set recursive well order ing of a subset of the natural numbers having the order type math alpha math . It is trivial to check that math omega math is recursive, the successor ordinal successor of a recursive ordinal is recursive, and the Set mathematics set of all recursive ordinals is closure mathematics closed downwards. The supremum of all recursive ordinals is called the Church Kleene ordinal and denoted by math omega CK 1 math . Indeed, an ordinal is recursive if and only if it is smaller than math omega CK 1 math . Since there are only countably many recursive relations, there are also only countable countably many recursive ordinals. Thus, math omega CK 1 math is countable. The recursive ordinals are exactly the ordinals that have an ordinal notation in Kleene s O Kleene s math mathcal O math . See also Arithmetical hierarchy Large countable ordinals Ordinal notation References Rogers, H. The Theory of Recursive Functions and Effective Computability , 1967. Reprinted 1987, MIT Press, ISBN 0 262 68052 1 paperback , ISBN 0 07 053522 1 Sacks, G. Higher Recursion Theory . Perspectives in mathematical logic, Springer Verlag, 1990. ISBN 0 387 19305 7 Category Set theory Category Computability theory Category Ordinal numbers settheory stub ... more details
Unreferenced date March 2009 A recursive call is a system call that must be completed before the completion of user s SQL statement. Basically, recursive calls are generated by Oracle Database Oracle internal sql statements to maintain changes to tables for internal processing. Reasons for Recursive Calls Recursive calls can be generated due to following reasons Dictionary cache is too small resulting in misses on cache Database Trigger Firing Performing DDL PL SQL blocks containing sql statements Category Computing terminology ... more details
In signal processing , a recursive filter is a type of filter signal processing filter which re uses one or more of its outputs as an input. This feedback typically results in an unending impulse response commonly referred to as infinite impulse response IIR , characterised by either exponential growth exponentially growing , exponential decay decaying , or sinusoid al signal output components. However, a recursive filter does not always have an infinite impulse response. Some implementations of moving average filter are recursive filters but with a Finite impulse response. Examples of recursive filters Kalman filter Category Signal processing electronics stub statistics stub economics stub ... more details
Unreferenced date December 2006 Orphan date February 2009 The recursive join is an operation used in relational databases , also sometimes called a fixed point join . It is a compound operation that involves repeating the join SQL join operation, typically accumulating more records each time, until a repetition makes no change to the results as compared to the results of the previous iteration . For example, if a database of family relationships is to be searched, and the record for each person has mother and father fields, a recursive join would be one way to retrieve all of a person s known ancestors first the person s direct parents records would be retrieved, then the parents information would be used to retrieve the grandparents records, and so on until no new records are being found. In this example, as in many real cases, the repetition involves only a single database table, and so is more specifically a recursive self join . Recursive joins can be very time consuming unless optimized through indexing, the addition of extra key fields, or other techniques. Recursive joins are highly characteristic of hierarchical data, and therefore become a serious issue with XML data. In XML, operations such as determining whether one element contains another are extremely common, and the recursive join is perhaps the most obvious way to implement them when the XML data is stored in a relational database. See also Join SQL Join Category Database theory Category Relational model Comp sci stub ... more details
Recursive partitioning is a statistics statistical method for multivariable analysis . ref name isbn0 412 04841 8 cite book author Breiman, Leo title Classification and Regression Trees publisher Chapman & Hall CRC location Boca Raton year 1984 pages isbn 0 412 04841 8 oclc doi ref Recursive partitioning creates a Decision tree learning decision tree that strives to correctly classify members of the population based on several dichotomous dependent variable s. This article focuses on recursive partitioning for medical diagnostic tests, but the technique has far wider applications. See Decision tree learning decision tree . As compared to regression analysis, which creates a formula that health care providers can use to calculate the probability that a patient has a disease, recursive partition creates a rule such as If a patient has finding x, y, or z they probably have disease q . A variation is Cox linear recursive partitioning . ref name pmid6501544 Advantages and disadvantages Compared to other multivariable methods, recursive partitioning has advantages and disadvantages. Advantages are Generates clinically more intuitive models that do not require the user to perform calculations. ref name pmid16149128 cite journal author James KE, White RF, Kraemer HC title Repeated split sample validation to assess logistic regression and recursive partitioning an application to the prediction ... analytic techniques advantages and disadvantages of recursive partitioning analysis journal ... KR, Beck JR title Experiments to determine whether recursive partitioning CART or an artificial neural ... modeling and recursive partitioning journal Methods of information in medicine volume 45 issue 1 ... recursive partitioning in research of diagnostic tests. ref name pmid15687312 cite journal author ... set by recursive partitioning methodology new insights into the relative merit of individual criteria ... 10 pages 588 96 year 1982 pmid 7110205 doi 10.1056 NEJM198209023071004 ref Goldman used recursive ... more details
refimprove date July 2010 A recursive acronym synonymous with metacronym , ref cite web url http www.urbandictionary.com define.php?term metacronym title UrbanDictionary.com Metacronym accessdate 2010 10 24 ref recursive initialism , and recursive backronym is an acronym and initialism acronym or initialism that recursion refers to itself in the expression for which it stands. The term was first used in print in April 1986. ref cite web url http www.wordspy.com words recursiveacronym.asp title WordSpy Recursive Acronym accessdate 2008 12 18 ref Computer related examples In computing , an early ... t Pico name for earliest versions of nano text editor nano text editor UIRA UIRA UIRA UIRA Isn t a Recursive ... Zinf Zinf Is Not Freeamp ZWEI ZWEI Was EINE Initially Mutually recursive or otherwise special The GNU Hurd project is named with a mutually recursive acronym Hurd stands for Hird of Unix Replacing Daemon ... project is another mutually recursive acronym Brain stands for Brian Relates Any Independent ... claims the distinction of being the first recursive anti acronym Citation needed date September 2011 ... that way. Most recursive acronyms are recursive on the first letter, which is therefore an arbitrary ..., which was originally Personal home page . However Yopy YOPY , Your own personal YOPY is recursive ... Recursive acronyms are not limited to computing terminology. For example TIARA TIARA is a recursive acronym ref .EXE magazine, November 1996 ref GURGA Group of Useless Recursive and Gurga Acronyms. ref ... Syndrome. RAS stands for Redundant Acronym Syndrome and is not recursive. The redundancy is in the name ... Strategical Multiple Operation Systems, from the video game series Xenosaga . A recursive initialism ..., recursive or otherwise, they may appear to be recursive acronyms, because of mnemonic ... 2 JargonFile See also Wiktionary recursive acronym RAS syndrome Redundant Acronym Syndrome syndrome Acronym s Backronym s Anti acronym DEFAULTSORT Recursive Acronym Category Acronyms Recursive Category ... more details
Orphan date November 2006 When number generally large number is represented in a finite alphabet set, and it cannot be represented by just one member of the set, Recursive indexing is used. Recursive indexing itself is a method to write the successive differences of the number after extracting the maximum value of the alphabet set from the number, and continuing recursively till the difference falls in the range of the set. Recursive indexing with a 2 letter alphabet is called Unary code . Encoding To encode a number N , keep reducing the maximum element of this set S sub max sub from N and output S max for each such difference, stopping when the number lies in the half closed half open range 0 S sub max sub . Example Let set S 0 1 2 3 4 10 , be a 11 element set, and we have to recursively index the value N 49. According to this method, we need to keep removing 10 from 49, and keep proceeding till we reach a number in the 0 10 range. So the values are 10 N 49 10 39 , 10 N 39 10 29 , 10 N 29 10 19 , 10 N 19 10 9 , 9. Hence the recursively indexed sequence for N 49 with set S , is 10,10,10,10,9. Decoding Keep adding all the elements of the index, stopping when the index value is between inclusive of ends the least and penultimate elements of the set S . Example Continuing from above example we have 10 10 10 10 9 49. Uses This technique is most commonly used in Run length encoding systems to encode longer runs than the alphabet sizes permit. References Khalid Sayood, Data Compression 3rd ed, Morgan Kaufmann . Category Coding theory Category Data compression Category Lossless compression algorithms ... more details
In mathematics , logic , and formal system s, a primitive notion is an undefined concept. In particular, a primitive notion is not defined in terms of previously defined concepts, but is only motivated informally, usually by an appeal to Intuition knowledge intuition and everyday experience. In an axiomatic theory or other formal system , the role of a primitive notion is analogous to that of axiom . In axiomatic theories, the primitive notions are sometimes said to be defined by one or more axioms, but this can be misleading. Formal theories cannot dispense with primitive notions, under pain of infinite regress . Alfred Tarski explained the role of primitive notions as follows When we set out to construct a given discipline, we distinguish, first of all, a certain small group of expressions ... we call PRIMITIVE TERMS or UNDEFINED TERMS, and we employ them without explaining their meanings. At the same ... consideration, unless its meaning has first been determined with the help of primitive terms and of such expressions ... the fundamental concept of set is an example of a primitive notion. As Mary Tiles wrote The definition ... of a primitive, undefined, term. As evidence, she quotes Felix Hausdorff A set is formed by the grouping ... an axiomatic system begins with its axiom s, the primitive notions may not be explicitly stated. Susan Haak 1978 wrote, A set of axioms is sometimes said to give an implicit definition of its primitive terms. Examples . In Naive set theory , the empty set is a primitive notion. To assert that it exists would be an implicit axiom . Peano arithmetic , the successor function and the number zero are primitive notions. Axiomatic system Axiomatic systems , the primitive notions will depend upon the set ... the primitive notions are point, line, plane, congruence, betweeness and incidence . Euclidean geometry , under Giuseppe Peano Peano s axiom system the primitive notions are point, segment and motion ... Tiles 2004 The Philosophy of Set Theory , page 99 DEFAULTSORT Primitive Notion Category Mathematical ... more details
In mathematics , a primitive root may mean either a primitive root modulo n in modular arithmetic , or a primitive nth root of unity amongst the solutions of x sup n sup 1 in a field mathematics field See also primitive element disambiguation mathdab ... more details
and PrimitiveRecursive Degrees, Transactions of the American Mathematical Society , v. 92, pp. 85 ...In computability theory , super recursive algorithms are a generalization of ordinary algorithm s that are more ..., whose book Super recursive algorithms develops their theory and presents several mathematical ... properties of recursive algorithms and their computations. In a similar way, mathematical models of super recursive algorithms, such as inductive Turing machines, allow researchers to find properties of super recursive algorithms and their computations. Burgin, as well as other researchers including ... Wiedermann who studied different kinds of super recursive algorithms and contributed to the theory of super recursive algorithms, have argued that super recursive algorithms can be used to disprove ... community and is not widely accepted. Definition Burgin 2005 13 uses the term recursive algorithms for algorithm ... sense. Then a super recursive class of algorithms is a class of algorithms in which it is possible to compute functions not computable by any Turing machine Burgin 2005 107 . Super recursive algorithms ... description of such a process. Thus a super recursive algorithm defines a computational process including processes of input and output that cannot be realized by recursive algorithms. Burgin ... 2002 Hagar and Korolev 2007 . Super recursive algorithms are also related to algorithmic schemes , which are more general than super recursive algorithms. Burgin argues 2005 115 that it is necessary to make a clear distinction between super recursive algorithms and those algorithmic schemes that are not algorithms. Under this distinction, some types of hypercomputation are obtained by super recursive ... by algorithmic schemas, e.g., infinite time Turing machines. This explains how works on super recursive algorithms are related to hypercomputation and vice versa. According to this argument, super recursive ... recursive algorithms include Burgin 2005 132 limiting recursive functions and limiting partial ... more details
Future Primitive may refer to Future Primitive band , from Southern California Future Primitive and Other Essays , a collection of essays by anarchist John Zerzan Future Primitive The New Ecotopias , a short story collection edited by Kim Stanley Robinson Future Primitive album Future Primitive album , the fifth album by Australian rock band The Vines A skateboarding video by Powell Peralta Filmography Powell Peralta disambig ... more details
In mathematics, the term primitive element can mean Primitive root modulo n Primitive root modulo n , in number theory Primitive element field theory , an element that generates a given field extension Primitive element finite field , an element that generates the multiplicative group of a finite field in a Hopf algebra , an element X on which the comultiplication has the value X X 1 1 X in a free group , an element of a free generating set See also primitive root disambiguation mathdab ... more details
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