Relevant bibliographies by topics / Primitive recursive

Contents

  1. Journal articles
  2. Dissertations / Theses
  3. Book chapters
  4. Conference papers

Academic literature on the topic 'Primitive recursive'

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Published: 4 June 2021
Last updated: 1 February 2022

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Journal articles on the topic "Primitive recursive"

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Severin, Daniel E. "Unary primitive recursive functions." Journal of Symbolic Logic 73, no. 4 (2008): 1122–38. http://dx.doi.org/10.2178/jsl/1230396909.

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AbstractIn this article, we study some new characterizations of primitive recursive functions based on restricted forms of primitive recursion, improving the pioneering work of R. M. Robinson and M. D. Gladstone. We reduce certain recursion schemes (mixed/pure iteration without parameters) and we characterize one-argument primitive recursive functions as the closure under substitution and iteration of certain optimal sets.
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Urzyczyn, Pawel. "Primitive Recursion with Existential Types1." Fundamenta Informaticae 19, no. 1-2 (1993): 201–22. http://dx.doi.org/10.3233/fi-1993-191-209.

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We consider computability over abstract structures with help of primitive recursive definitions (an appropriate modification of Gödel’s system T). Unlike the standard approach, we do not assume any fixed representation of integers, but instead we allow primitive recursion to be polymorphic, so that iteration is performed with help of counters viewed as objects of an abstract type Int of arbitrary (hidden) implementation. This approach involves the use of existential quantification in types, following the ideas of Mitchell and Plotkin. We show that the halting problem over finite interpretations is primitive recursive for each program involving primitive recursive definitions. Conversely, each primitive recursive set of interpretations is defined by the termination property of some program.
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Kalimullin, I. Sh, and A. G. Melnikov. "Punctual Categoricity Relative to a Computable Oracle." Lobachevskii Journal of Mathematics 42, no. 4 (2021): 735–42. http://dx.doi.org/10.1134/s1995080221040107.

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Abstract We are studying the punctual structures, i.e., the primitive recursive structures on the whole set of integers. The punctual categoricity relative to a computable oracle $$f$$ means that between any two punctual copies of a structure there is an isomorphism which togeteher with its inverse can be derived via primitive recursive schemes augmented with $$f$$. We will prove that the punctual categoricity relative to a computable oracle can hold only for finitely generated or locally finite structures. We will show that the punctual categoricity of finitely generated structures is exhaused by the computable oracles with primitive recursive graph. We also present an example of locally finite structure where the punctual categoricity is provided by a primitive recursively bounded computable oracle.
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Chen, Qingliang, Kaile Su, and Xizhong Zheng. "Primitive recursive real numbers." MLQ 53, no. 4-5 (2007): 365–80. http://dx.doi.org/10.1002/malq.200710005.

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Colson, Loïc. "About primitive recursive algorithms." Theoretical Computer Science 83, no. 1 (1991): 57–69. http://dx.doi.org/10.1016/0304-3975(91)90039-5.

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KOHLENBACH, ULRICH. "A UNIFORM QUANTITATIVE FORM OF SEQUENTIAL WEAK COMPACTNESS AND BAILLON'S NONLINEAR ERGODIC THEOREM." Communications in Contemporary Mathematics 14, no. 01 (2012): 1250006. http://dx.doi.org/10.1142/s021919971250006x.

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We apply proof-theoretic techniques of "proof mining" to obtain an effective uniform rate of metastability in the sense of Tao for Baillon's famous nonlinear ergodic theorem in Hilbert space. In fact, we analyze a proof due to Brézis and Browder of Baillon's theorem relative to the use of weak sequential compactness. Using previous results due to the author we show the existence of a bar recursive functional Ω* (using only lowest type bar recursion B0, 1) providing a uniform quantitative version of weak compactness. Primitive recursively in this functional (and hence in T0 + B0, 1) we then construct an explicit bound φ on for the metastable version of Baillon's theorem. From the type level of φ and another result of the author it follows that φ is primitive recursive in the extended sense of Gödel's T. In a subsequent paper also Ω* will be explicitly constructed leading to the refined complexity estimate φ ∈ T4.
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Kalimullin, I. Sh, and R. Miller. "Primitive recursive fields and categoricity." Algebra i logika 58, no. 1 (2019): 132–38. http://dx.doi.org/10.33048/alglog.2019.58.108.

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Damnjanovic, Zlatan. "Strictly primitive recursive realizability, I." Journal of Symbolic Logic 59, no. 4 (1994): 1210–27. http://dx.doi.org/10.2307/2275700.

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AbstractA realizability notion that employs only primitive recursive functions is defined, and, relative to it, the soundness of the fragment of Heyting Arithmetic (HA) in which induction is restricted to formulae is proved. A dual concept of falsifiability is proposed and an analogous soundness result is established for a further restricted fragment of HA.
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Kalimullin, I. Sh, and R. Miller. "Primitive Recursive Fields and Categoricity." Algebra and Logic 58, no. 1 (2019): 95–99. http://dx.doi.org/10.1007/s10469-019-09527-1.

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Hasan, Sartaj Ul, Daniel Panario, and Qiang Wang. "Nonlinear vectorial primitive recursive sequences." Cryptography and Communications 10, no. 6 (2017): 1075–90. http://dx.doi.org/10.1007/s12095-017-0265-2.

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Dissertations / Theses on the topic "Primitive recursive"

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Spoors, Elliott John. "A hierarchy of ramified theories below primitive recursive arithmetic." Thesis, University of Leeds, 2010. http://etheses.whiterose.ac.uk/1554/.

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The arithmetical theory EA(I;O) developed by Çagman, Ostrin and Wainer ([18] and [48]) provides a formal setting for the variable separation of Bellantoni-Cook predicative recursion [6]. As such, EA(I;O) separates variables into outputs, which are quantified over, and inputs, for which induction applies. Inputs remain free throughout giving inductions in EA(I;O) a pointwise character termed predicative induction. The result of this restriction is that the provably recursive functions are the elementary functions. An infinitary analysis brings out a connection to the Slow-Growing Hierarchy yielding є0 as the appropriate proof-theoretic ordinal in a pointwise sense. Chapters 1 and 2 are devoted to an exposition of these results. In Chapter 3 a new principle of 1-closure is introduced in constructing a conservative extension of EA(I;O) named EA1. This principle collapses the variable separation in EA(I;O) and allows quantification over inputs by acting as an internalised ω-rule. EA1 then provides a natural setting to address the problem of input substitution in ramified theories. Chapters 4 and 5 introduce a hierarchy of theories based upon alternate additions of the predicative induction and ∑1-closure principles. For 0 < k є N, the provably recursive functions of the theories EAk are shown to be the Grzegorczyk classes Ek+2. Upper bounds are obtained via embeddings into appropriately layered infinitary systems with carefully controlled bounding functions for existential quantifiers. The theory EA-ω, defined by closure under finite applications of these two principles, is shown to be equivalent to primitive recursive arithmetic. The hierarchy generated may be considered as an implicit ramification of the sub-system of Peano Arithmetic which restricts induction to ∑1-formulae.
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Gomes, Victor pereira. "Funções recursivas primitivas: caracterização e alguns resultados para esta classe de funções." Universidade Federal da Paraíba, 2016. http://tede.biblioteca.ufpb.br:8080/handle/tede/8514.

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Submitted by Maike Costa (maiksebas@gmail.com) on 2016-08-10T14:17:41Z No. of bitstreams: 1 arquivo total.pdf: 975005 bytes, checksum: 6f8194b9c0cb9c0bbd07b1d2b0ba4b9e (MD5)<br>Made available in DSpace on 2016-08-10T14:17:41Z (GMT). No. of bitstreams: 1 arquivo total.pdf: 975005 bytes, checksum: 6f8194b9c0cb9c0bbd07b1d2b0ba4b9e (MD5) Previous issue date: 2016-06-21<br>Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES<br>The class of primitive recursive functions is not a formal version to the class of algorithmic functions, we study this special class of numerical functions due to the fact of that many of the functions known as algorithmic are primitive recursive. The approach on the class of primitive recursive functions aims to explore this special class of functions and from that, present solutions for the following problems: (1) given the class of primitive recursive derivations, is there an algorithm, that is, a mechanical procedure for recognizing primitive recursive derivations? (2) Is there a universal function for the class of primitive recursive functions? If so, is this function primitive recursive? (3) Are all the algorithmic functions primitive recursive? To provide solutions to these issues, we base on the hypothetical-deductive method and argue based on the works of Davis (1982), Mendelson (2009), Dias e Weber (2010), Rogers (1987), Soare (1987), Cooper (2004), among others. We present the theory of Turing machines which is a formal version to the intuitive notion of algorithm, and after that the famous Church-Turing tesis which identifies the class of algorithmic functions with the class of Turing-computable functions. We display the class of primitive recursive functions and show that it is a subclass of Turing-computable functions. Having explored the class of primitive recursive functions we proved as results that there is a recognizer algorithm to the class of primitive recursive derivations; that there is a universal function to the class of primitive recursive functions which does not belong to this class; and that not every algorithmic function is primitive recursive.<br>A classe das funções recursivas primitivas não constitui uma versão formal para a classe das funções algorítmicas, estudamos esta classe especial de funções numéricas devido ao fato de que muitas das funções conhecidas como algorítmicas são recursivas primitivas. A abordagem acerca da classe das funções recursivas primitivas tem como objetivo explorar esta classe especial de funções e, a partir disto, apresentar soluções para os seguintes problemas: (1) dada a classe das derivações recursivas primitivas, há um algoritmo, ou seja, um procedimento mecânico, para reconhecer derivações recursivas primitivas? (2) Existe uma função universal para a classe das funções recursivas primitivas? Se sim, essa função é recursiva primitiva? (3) Toda função algorítmica é recursiva primitiva? Para apresentar soluções para estas questões, nos pautamos no método hipotético-dedutivo e argumentamos com base nos manuais de Davis (1982), Mendelson (2009), Dias e Weber (2010), Rogers (1987), Soare (1987), Cooper (2004), entre outros. Apresentamos a teoria das máquinas de Turing, que constitui uma versão formal para a noção intuitiva de algoritmo, e, em seguida, a famosa tese de Church-Turing, a qual identifica a classe das funções algorítmicas com a classe das funções Turing-computáveis. Exibimos a classe das funções recursivas primitivas, e mostramos que a mesma constitui uma subclasse das funções Turing-computáveis. Tendo explorado a classe das funções recursivas primitivas, como resultados, provamos que existe um algoritmo reconhecedor para a classe das derivações recursivas primitivas; que existe uma função universal para a classe das funções recursivas primitivas a qual não pertence a esta classe; e que nem toda função algorítmica é recursiva primitiva.
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Perrinel, Matthieu. "Investigating the expressivity of linear logic subsystems characterizing polynomial time." Thesis, Lyon, École normale supérieure, 2015. http://www.theses.fr/2015ENSL1001/document.

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La complexité implicite est la caractérisation de classes de complexité par des restrictions syntaxiques sur des modèles de calcul. Plusieurs sous-systèmes de la logique linéaire caractérisant le temps polynomial ont été définis: ces systèmes sont corrects (les termes normalisent en temps polynomial) et complets (il est possible de simuler une machine de Turing pendant un nombre polynomial d'étapes). Un des buts sur le long terme est de donner statiquement des bornes de complexité. C’est pourquoi nous cherchons les caractérisations du temps polynomial les plus expressives possible. Notre principal outil est la sémantique des contextes: des jetons voyagent à travers le réseau selon certaines règles. Les chemins définis par ces jetons représentent la réduction du réseau. Contrairement aux travaux précédents, nous ne définissons pas directement des sous-systèmes de la logique linéaire. Nous définissons d'abord des relations -&gt; sur les sous-termes des réseaux de preuves tel que: B -&gt; C ssi ”le nombre de copies de B dépend du nombre de copies de C”. L’acyclicité de -&gt; borne le nombre de copies de chaque sous-terme, donc la complexité du terme. Ensuite nous définissons des sous-systèmes de la logique linéaire assurant l’acyclicité de -&gt;. Nous étudions aussi des caractérisations du temps élémentaire et primitif récursif. Dans le but d’adapter nos sous-systèmes de la logique linéaire à des langages plus riches, nous adaptons la sémantique des contextes aux réseaux d’interaction, utilisés comme langage cible pour de petits langage de programmation. Nous utilisons cette sémantique des contexte pour définir une sémantique dénotationnelle sur les réseaux d’interactions<br>Implicit computational complexity is the characterization of complexity classes by syntactic restrictions on computation models. Several subsystems of linear logic characterizing polynomial time have been defined : these systems are sound (terms normalize in polynomial time) and complete (it is possible to simulate a Turing machine during a polynomial number of steps). One of the long term goals is to statically prove complexity bounds. This is why we are looking for the most expressive characterizations possible. Our main tool is context semantics : tokens travel across proof-nets (programs of linear logic) according to some rules. The paths defined by these tokens represent the reduction of the proof-net.Contrary to previous works, we do not directly define subsystems of linear logic. We first define relations -&gt; on subterms of proof-nets such that: B -&gt; C means \the number of copies of B depends on the number of copies of C". The acyclicity of -&gt; allows us to bound the number of copies of any subterm, this bounds the complexity of the term. Then, we define subsystems of linear logic guaranteeing the acyclicity of -&gt;. We also study characterizations of elementary time and primitive recursive time. In orderto adapt our linear logic subsystems to richer languages, we adapt the context semantics to interaction nets, used as a target language for small programming languages. We use this context semantics to define a denotational semantics on interaction nets
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Valarcher, Pierre. "Contribution a l'etude du comportement intentionnel des algorithmes : le cas de la recursion primitive." Paris 7, 1996. http://www.theses.fr/1996PA077143.

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Nous etudions dans cette these la maniere dont un algorithme ecrit sur sa sortie en fonction de ce qu'il a deja lu sur ses entrees (ce qu'on appelle comportement intentionnel). Ce travail complete des travaux inities par l. Colson et t. Coquand qui ont etudie certains systemes fonctionnels. Nous etudions le comportement intentionnel des algorithmes definissables dans differents langages: le langage de la recursion primitive (pr), le langage de la recursion avec substitution de parametres (prv) et le langage de la recursion sur les listes (prl). Nous donnons une caracterisation complete de la classe des fonctions qui sont le comportement intentionnel d'algorithmes pr et nous montrons que l'on obtient toutes les fonctions primitives recursives (p. R) unaires croissantes ainsi qu'une large classe de fonctions p. R. Sequentielles comme comportements intentionnels de prv et prl. Nous donnons enfin, differentes inclusions concernant les comportements de ces langages. Ce travail a ete mene en etudiant la semantique denotationnelle de ces differents langages et en implantant les differents algorithmes dans le langage fonctionnel haskell
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Glimming, Johan. "Primitive Direcursion and Difunctorial Semantics of Typed Object Calculus." Doctoral thesis, Stockholm : Numerisk analys och datalogi (KTH CSC), Stockholms universitet, 2007. http://urn.kb.se/resolve?urn=urn:nbn:se:su:diva-7208.

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MORENO, SOCIAS GUILLERMO. "Autour de la fonction de hilbert-samuel (escaliers d'ideaux polynomiaux)." Palaiseau, Ecole polytechnique, 1991. http://www.theses.fr/1991EPXX0034.

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Les escaliers d'ideaux dans un anneau de polynomes (appeles aussi order ideal of monomials) sont des objets plus fins que les fonctions de hilbert-samuel, obtenus en introduisant un ordre sur le monomes. Nous etudions ici deux questions de geometrie algebrique effective, en considerant deux types opposes d'escaliers: generiques et compresses. Le calcul des bases standard (ou bases de brobner), peut etre tres couteux (doublement exponentiel). Afin de reduire cette complexite, en nous inspirant d'une idee de giusti nous distinguons les syzygies structurellement nulles de celles qui le sont accidentellement. L'etude des premieres conduit a enoncer plusieurs conjectures, que nous demontrons pour l'ordre lexicographique inverse dans le cas des intersections completes. Nous obtenons en particulier des theoremes de structure qui decrivent explicitement des escaliers generiques. Nous donnons alors diverses heuristiques et strategies pour simplifier l'algorithme de calcul des bases standard dans les cas suffisamment generiques. En 1971, seidenberg avait etudie une question de ntherianite effective (partiellement reposee par mora en 1991): dans un anneau de polynomes a n variables on veut borner la longueur d'une chaine ascendante d'ideaux, ou le k-ieme ideal peut etre engendre en degre au plus f(k). En construisant une chaine maximale avec des escaliers compresses, nous montrons qu'on a une borne recursive primitive en f pour tout n. Nous demontrons aussi qu'il n'y a pas de borne recursive primitive en n, meme si l'on se restreint a des fonctions f a croissance lineaire (la fonction d'ackermann apparait ici inopinement). Plusieurs systemes de calcul formel (maple, macaulay, macsyma, etc. ) ont ete utilises. Nous avons ecrit de nombreux programmes, surtout en lisp: calcul de bases standard (avec choix d'ordres, criteres, strategies et traces), fonctions de hilbert-samuel, complexes de koszul et suites spectrales, calcul dans des algebres quotient, dessins d'escaliers en postscript, etc. )
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Book chapters on the topic "Primitive recursive"

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Weihrauch, Klaus. "Primitive Recursive and μ-Recursive Functions." In Computability. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/978-3-642-69965-8_4.

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Kalimullin, Iskander. "On Primitive Recursive Permutations." In Computability and Models. Springer US, 2003. http://dx.doi.org/10.1007/978-1-4615-0755-0_10.

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Colson, Loïc. "About primitive recursive algorithms." In Automata, Languages and Programming. Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/bfb0035761.

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Plisko, Valery. "On Primitive Recursive Realizabilities." In Computer Science – Theory and Applications. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11753728_31.

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Kulyukin, Vladimir A. "Chess Is Primitive Recursive." In Transactions on Computational Science and Computational Intelligence. Springer International Publishing, 2021. http://dx.doi.org/10.1007/978-3-030-70873-3_30.

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Agerholm, Sten. "Non-primitive recursive function definitions." In Higher Order Logic Theorem Proving and Its Applications. Springer Berlin Heidelberg, 1995. http://dx.doi.org/10.1007/3-540-60275-5_54.

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Nelson, Neal. "Primitive recursive functional with dependent types." In Lecture Notes in Computer Science. Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/3-540-55511-0_6.

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Stirling, Colin. "Deciding DPDA Equivalence Is Primitive Recursive." In Automata, Languages and Programming. Springer Berlin Heidelberg, 2002. http://dx.doi.org/10.1007/3-540-45465-9_70.

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Asser, Günter. "Primitive recursive word-functions of one variable." In Computation Theory and Logic. Springer Berlin Heidelberg, 1987. http://dx.doi.org/10.1007/3-540-18170-9_150.

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Zucker, J. I. "Primitive Recursive Selection Functions over Abstract Algebras." In Logical Approaches to Computational Barriers. Springer Berlin Heidelberg, 2006. http://dx.doi.org/10.1007/11780342_61.

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Conference papers on the topic "Primitive recursive"

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Enes, Aaron R., and Wayne J. Book. "Recursive algorithm for motion primitive estimation." In 2011 IEEE International Conference on Robotics and Automation (ICRA 2011). IEEE, 2011. http://dx.doi.org/10.1109/icra.2011.5980456.

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Figueira, Diego, Santiago Figueira, Sylvain Schmitz, and Philippe Schnoebelen. "Ackermannian and Primitive-Recursive Bounds with Dickson's Lemma." In 2011 26th Annual IEEE Symposium on Logic in Computer Science (LICS 2011). IEEE, 2011. http://dx.doi.org/10.1109/lics.2011.39.

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Asperti, Andrea. "The Speedup Theorem in a Primitive Recursive Framework." In POPL '15: The 42nd Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages. ACM, 2015. http://dx.doi.org/10.1145/2676724.2693178.

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Wehage, R. A. "Solution of Multibody Dynamics Using Natural Factors and Iterative Refinement: Part I — Open Kinematic Loops." In ASME 1989 Design Technical Conferences. American Society of Mechanical Engineers, 1989. http://dx.doi.org/10.1115/detc1989-0115.

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Abstract An O(n) methodology employing block matrix partitioning and recursive projection to solve multibody equations of motion coupled by a sparse connectivity matrix was developed in (Wehage 1988, 1989, Wehage and Shabana, 1989). These primitive equations, which include all joint generalized and absolute coordinates and constraint reaction forces, are easily obtained from free body diagrams. The corresponding recursive algorithms isolate the generalized joint accelerations for numerical integration and offer the best computational advantage when solving long kinematic chains on serial processors. Recursion, however, precludes effective exploitation of vector or parallel processors. Therefore this paper explores less recursive algorithms by applying the inverse of joint connectivity to eliminate absolute accelerations and constraint forces yielding a generalized system of equations. The resulting positive definite generalized inertia matrix is first represented symbolically as a product of sparse matrices, of which some are singular and then as the product of nonsingular factors obtained recursively. This algorithm has overhead ranging from O(n2) to O(n) depending on the degree of system parallelism. Incorporating iterative refinement and exploiting parallel and vector processing makes this approach competitive for many applications.
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Mahadevan, Sai Veerya, Yuuki Takano, and Atsuko Miyaji. "PRSafe: Primitive Recursive Function based Domain Specific Language using LLVM." In 2021 International Conference on Electronics, Information, and Communication (ICEIC). IEEE, 2021. http://dx.doi.org/10.1109/iceic51217.2021.9369763.

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Leroux, Jerome, and Sylvain Schmitz. "Reachability in Vector Addition Systems is Primitive-Recursive in Fixed Dimension." In 2019 34th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS). IEEE, 2019. http://dx.doi.org/10.1109/lics.2019.8785796.

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Kahrs, Stefan. "Genetic programming with primitive recursion." In the 8th annual conference. ACM Press, 2006. http://dx.doi.org/10.1145/1143997.1144160.

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Ambroszkiewicz, Stanislaw. "Primitive recursion on higher types." In 2015 Computer Science and Information Technologies (CSIT). IEEE, 2015. http://dx.doi.org/10.1109/csitechnol.2015.7358244.

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Ryzhikov, Vladislav, Przemyslaw Andrzej Walega, and Michael Zakharyaschev. "Data Complexity and Rewritability of Ontology-Mediated Queries in Metric Temporal Logic under the Event-Based Semantics." In Twenty-Eighth International Joint Conference on Artificial Intelligence {IJCAI-19}. International Joint Conferences on Artificial Intelligence Organization, 2019. http://dx.doi.org/10.24963/ijcai.2019/256.

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We investigate the data complexity of answering queries mediated by metric temporal logic ontologies under the event-based semantics assuming that data instances are finite timed words timestamped with binary fractions. We identify classes of ontology-mediated queries answering which can be done in AC0, NC1, L, NL, P, and coNP for data complexity, provide their rewritings to first-order logic and its extensions with primitive recursion, transitive closure or datalog, and establish lower complexity bounds.
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Ambler, S. J., R. L. Crole, and Alberto Momigliano. "A definitional approach to primitivexs recursion over higher order abstract syntax." In the 2003 workshop. ACM Press, 2003. http://dx.doi.org/10.1145/976571.976572.

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