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Relevant bibliographies by topics / Classes of recursive functions

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Academic literature on the topic 'Classes of recursive functions'

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Published: 4 June 2021

Last updated: 1 February 2022

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Journal articles on the topic "Classes of recursive functions"

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Wainer, Stanley S. "Accessible Recursive Functions." Bulletin of Symbolic Logic 5, no. 3 (September 1999): 367–88. http://dx.doi.org/10.2307/421185.

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AbstractThe class of all recursive functions fails to possess a natural hierarchical structure, generated predicatively from “within”. On the other hand, many (proof-theoretically significant) sub-recursive classes do. This paper attempts to measure the limit of predicative generation in this context, by classifying and characterizing those (predictably terminating) recursive functions which can be successively defined according to an autonomy condition of the form: allow recursions only over well-orderings which have already been “coded” at previous levels. The question is: how can a recursion code a well-ordering? The answer lies in Girard's theory of dilators, but is reworked here in a quite different and simplified framework specific to our purpose. The “accessible” recursive functions thus generated turn out to be those provably recursive in ( –CA)0.

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Stephan, Frank, and Thomas Zeugmann. "Learning classes of approximations to non-recursive functions." Theoretical Computer Science 288, no. 2 (October 2002): 309–41. http://dx.doi.org/10.1016/s0304-3975(01)00405-4.

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Mazzanti, Stefano. "Plain Bases for Classes of Primitive Recursive Functions." MLQ 48, no. 1 (January 2002): 93–104. http://dx.doi.org/10.1002/1521-3870(200201)48:1<93::aid-malq93>3.0.co;2-8.

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SEMIGRODSKIKH, A. P. "On Closed Classes of Primitive Recursive Functions, II." Multiple-Valued Logic 8, no. 2 (January 1, 2002): 183–91. http://dx.doi.org/10.1080/10236620215292.

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Kummer, Martin. "A learning-theoretic characterization of classes of recursive functions." Information Processing Letters 54, no. 4 (May 1995): 205–11. http://dx.doi.org/10.1016/0020-0190(95)00036-c.

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Volkov, S. A. "Generating some classes of recursive functions by superpositions of simple arithmetic functions." Doklady Mathematics 76, no. 1 (August 2007): 566–67. http://dx.doi.org/10.1134/s1064562407040217.

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AUSIELLO, G., and M. PROTASI. "LIMITING POLYNOMIAL APPROXIMATION OF COMPLEXITY CLASSES." International Journal of Foundations of Computer Science 01, no. 02 (June 1990): 111–22. http://dx.doi.org/10.1142/s0129054190000096.

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The concept of limiting approximation, formerly introduced by Gold for recursive functions, is applied to the polynomial level of complexity in order to determine meaningful characterizations of classes of functions and sets which are not (or which are not known to be) polynomially computable. In particular, characterizations of NP, PSPACE and other classes of elementary functions are provided in terms of limiting polynomial approximation. In addition trade-offs between the space required by the approximating functions and the rate of convergence of the approximation are shown.

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Zhukov, Vladimir V., and Sergey A. Lozhkin. "Asymptotically best method for synthesis of Boolean recursive circuits." Discrete Mathematics and Applications 30, no. 2 (April 28, 2020): 137–46. http://dx.doi.org/10.1515/dma-2020-0013.

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AbstractModels of multi-output and scalar recursive Boolean circuits of bounded depth in an arbitrary basis are considered. Methods for lower and upper estimates for the Shannon function for the complexity of circuits of these classes are provided. Based on these methods, an asymptotic formula for the Shannon function is put forward. Moreover, in the above classes of recursive circuits, upper estimates for the complexity of implementation of some functions and systems of functions used in applications are obtained.

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Calude, Cristian, and Gabriel Istrate. "Determining and stationary sets for some classes of partial recursive functions." Theoretical Computer Science 82, no. 1 (May 1991): 151–55. http://dx.doi.org/10.1016/0304-3975(91)90178-5.

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Rout, Ranjeet Kumar, Pabitra Pal Choudhury, and Sudhakar Sahoo. "Classification of Boolean Functions Where Affine Functions Are Uniformly Distributed." Journal of Discrete Mathematics 2013 (October 31, 2013): 1–12. http://dx.doi.org/10.1155/2013/270424.

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The present paper on classification of -variable Boolean functions highlights the process of classification in a coherent way such that each class contains a single affine Boolean function. Two unique and different methods have been devised for this classification. The first one is a recursive procedure that uses the Cartesian product of sets starting from the set of one variable Boolean functions. In the second method, the classification is done by changing some predefined bit positions with respect to the affine function belonging to that class. The bit positions which are changing also provide us information concerning the size and symmetry properties of the classes/subclasses in such a way that the members of classes/subclasses satisfy certain similar properties.

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Dissertations / Theses on the topic "Classes of recursive functions"

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Cooper, D. "Classes of low complexity." Thesis, University of Oxford, 1986. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.375251.

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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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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.
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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Ferizis, George Computer Science &amp Engineering Faculty of Engineering UNSW. "Mapping recursive functions to reconfigurable hardware." Awarded by:University of New South Wales. Computer Science and Engineering, 2005. http://handle.unsw.edu.au/1959.4/23366.

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Reconfigurable computing is a method of development that provides a developer with the ability to reprogram a hardware device. In the specific case of FPGAs this allows for rapid and cost effective implementation of hardware devices when compared to standard a ASIC design, coupled with an increase in performance when compared to software based solutions. With the advent of development tools such as Celoxica's DK package and Xilinx's Forge package, that support languages traditionally associated with software development, a change in the skill sets required to develop FPGA solutions from hardware designers to software programmers is possible and perhaps desirable to increase the adoption of FPGA technologies. To support developers with these skill sets tools should closely mirror current software development tools in terms of language, syntax and methodology, while at the same time both transparently and automatically take advantage of as much of the increased performance that reconfigurable architectures can provide over traditional software architectures by utilizing the parallelism and the ability to create arbitrary depth pipelines which is not present in traditional microprocessor designs. A common feature of many programming languages that is not supported by many higher level design tools is recursion. Recursion is a powerful method used to elegantly describe many algorithms. Recursion is typically implemented by using a stack to store arguments, context and a return address for function calls. This however limits the controlling hardware to running only a single function at any moment which eliminates an algorithm's ability to take advantage of the parallelism available between successive iterations of a recursive function. This squanders the high amount of parallelism provided by the resources on the FPGA thus reducing the performance of the recursive algorithm. This thesis presents a method to address the lack of support for recursion in design tools that exploits the parallelism available between recursive calls. It does this by unrolling the recursion into a pipeline, in a similar manner to the pipeline obtained from loop unrolling, and then streaming the data through the resulting pipeline. However essential differences between loops and recursive functions such as multiple recursive calls in a function, and hence multiple unrollings, and post-recursive statements add further complexity to the issue of unrolling as the pipeline may take a non-linear shape and contain heterogeneous stages. Unrolling the recursive function on the FPGA increases the parallelism available, however the depth of the pipline and therefore the amount of parallelism available, is limited by the finite resources on the FPGA. To make efficient use of the resources on the FPGA the system must be able to unroll the function in a way to best suit the input but also must ensure that the function is not unrolled past its maximum recursive depth. A trivial solution such as unrolling on-demand introduces a latency into the system when a further instance of the function is unrolled that reduces overall performance. To reduce this penalty it is desirable for the system to be able to predict the behaviour of the recursive function based on the input data and unroll the function to a suitable length prior to it being required. Accurate prediction is possible in cases where the condition for recursion is a simple function on the arguments, however in cases where the condition for recursion is based on complex functions, such as the entire recursive function, accurate prediction is not possible. In situations such as this a heuristic is used which provides a close approximation to the correct depth of recursion at any given time. This prediction allows the system to reduce the performance penalty from real time unrolling without over utilization of the the FPGA resources. Results obtained demonstrate the increase in performance for various recursive functions obtained from the increased parallelism, when compared to a stack based implementation on the same device. In certain instances due to constraints on hardware availability results were gained from device simulation using a simulator developed for this purpose. Details of this simulator are presented in this thesis.

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Francis, Johanna Leigh 1970. "Three essays in recursive utility functionals." Thesis, McGill University, 1992. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=61285.

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Three essays in the study recursive utility are presented. The first is an exposition of the extant recursive utility literature. A correspondence is drawn between the discrete time axioms for recursive utility in Koopmans (1960) and the continuous time framework in Epstein (1987b). The second essay investigates the method for endogenizing the rate of time preference given in Uzawa (1968). It is shown that when applied to non-autonomous systems, the Uzawa transformation generates errors in first order conditions. We provide a simple method for extending the Uzawa transformation to non-autonomous systems. These results are applied to two stochastic optimal control problems in the third essay. In the first problem a consumer optimally allocates consumption of a given cake whose size is unknown. With an endogenous rate of time preference, it is shown that the consumption profile may be increasing monotonic under a given set of assumptions. The second problem incorporates an endogenous rate of time preference into a stochastic optimal growth model.

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House, Robert Simpson. "Airy functions and the Recursive Ray Acoustics Algorithm." Thesis, Monterey, Calif. : Springfield, Va. : Naval Postgraduate School ; Available from National Technical Information Service, 1994. http://handle.dtic.mil/100.2/ADA290182.

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Thesis (M.S. in Electrical Engineering) Naval Postgraduate School, December 1994.
Thesis advisor(s): Lawrence J. Ziomek. "December 1994." Includes bibliographical references. Also available online.

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McVeigh, Brian. "Multiple functions in equivalence classes." Thesis, University of Ulster, 2004. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.414095.

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Clouâtre, André. "Implementation and applications of recursively defined relations." Thesis, McGill University, 1987. http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=75694.

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In relational algebra, a recursive relation R is defined by an equation of the form R = f(R), where f(R) is a positive relational algebra expression. Such an equation can be solved by applying a general closure operator. Although some optimization is possible, the performance obtained using this approach is very dependent on the form of the equation which defines R. Principally for this reason, we have developed specialized closure operators for relations which are solutions to problems of practical importance such as transitive closure, accessibility, shortest path, bill-of-materials, and deductions by containment comparisons.
This approach has led to the following general results: (1) design, classification, and analysis of many iterative methods for evaluating recursive relations, as well as analysis of experimental results; (2) formalization of the concept of iterative evaluation of a relation; (3) demonstration that domain algebra can be used to solve problems of concatenation and aggregation of the information associated with a recursive structure; (4) proof that relational division and general containment joins are left-monotone.
More specific results consist of a collection of original algorithms which run well on secondary storage, as shown by simulations. Among them, we wish to emphasize the differencing logarithmic transitive closure (TC) algorithms, which are superior to the previously known relational TC algorithms, and the shortest path algorithms, which are in fact generic algorithms for path algebra problems.

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Kabanets, Valentine. "Nonuniformly hard Boolean functions and uniform complexity classes." Thesis, National Library of Canada = Bibliothèque nationale du Canada, 2001. http://www.collectionscanada.ca/obj/s4/f2/dsk3/ftp04/NQ58599.pdf.

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Darus, M. "Extreme problems for certain classes of analytic functions." Thesis, Swansea University, 1995. http://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.636350.

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This thesis is concerned with extreme problems for certain classes of analytic functions. In many cases, the classes of functions considered form proper subclasses of the class S of normalised analytic functions which are univalent in the unit disc D. In Chapter 1, we present some definitions and known results which are required in subsequent chapters. In Chapter 2, we state some known results concerning the so-called Fekete-Szegö Theorem. We give some extensions and new results in the case of close-to-convex functions. Chapter 3 contains some miscellaneous Fekete-Szegö Theorems. In this chapter, we introduce a new class of analytic functions, which we call logarithmically convex. These functions are a natural analogue to the so-called α-convex functions, studied extensively over the last decade or so. Some extreme coefficient problems are solved for logarithmically convex functions. The final chapter deals with subordination. We apply a lemma of Miller and Mocanu to obtain a series of best possible subordination theorems when the super-ordinate function lies in a sector, rather than the usual half-plane. A consequence of one such result is that the logarithmically convex functions defined in Chapter 3 form a subset of the starlike functions and are thus univalent in D.

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Pedron, Mark [Verfasser]. "Zero Partition Cycles : A Recursive Formula for Characteristic Classes of Surface Bundles / Mark Pedron." Bonn : Universitäts- und Landesbibliothek Bonn, 2017. http://d-nb.info/1132711517/34.

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Books on the topic "Classes of recursive functions"

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Sanchis, Luis E. Recursive functionals. Amsterdam: North-Holland, 1992.

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Murawski, Roman. Recursive Functions and Metamathematics. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-017-2866-9.

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Recursive algorithms. Norwood, N.J: Ablex Pub. Corp., 1994.

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Marcet, Albert. Recursive contracts. Florence: European University Institute, 1998.

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Zilles, Sandra. Uniform learning of recursive functions. Berlin: Akademische Verlagsgesellschaft Aka, 2003.

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Theory of recursive functions and effective computability. Cambridge, Mass: MIT Press, 1987.

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Hong, Chew Soo. Recursive utility under uncertainty. Toronto: Dept. of Economics and Institute for Policy Analysis, University of Toronto, 1990.

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Rogers, Hartley. Theory of recursive functions and effective computability. Cambridge, Mass: MIT Press, 1987.

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Stokey, Nancy L. Recursive Methods in Economic Dynamics. Cambridge, MA, USA: Harvard University Press, 1989.

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J, Sargent Thomas, ed. Recursive macroeconomic theory. 3rd ed. Cambridge, MA: MIT Press, 2012.

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Book chapters on the topic "Classes of recursive functions"

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Apsītis, Kalvis, Rūsinš Freivalds, Mārtinš Krikis, Raimonds Simanovskis, and Juris Smotrovs. "Unions of identifiable classes of total recursive functions." In Analogical and Inductive Inference, 99–107. Berlin, Heidelberg: Springer Berlin Heidelberg, 1992. http://dx.doi.org/10.1007/3-540-56004-1_7.

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Wette, Elisabeth. "Sequential representation of primitive recursive functions, and complexity classes." In Lecture Notes in Computer Science, 422–37. Berlin, Heidelberg: Springer Berlin Heidelberg, 1990. http://dx.doi.org/10.1007/3-540-52753-2_56.

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Ambainis, Andris, and Juris Smotrovs. "Enumerable classes of total recursive functions: Complexity of inductive inference." In Lecture Notes in Computer Science, 10–25. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-58520-6_50.

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Nessel, Jochen. "Learnability of Enumerable Classes of Recursive Functions from “Typical” Examples." In Lecture Notes in Computer Science, 264–75. Berlin, Heidelberg: Springer Berlin Heidelberg, 1999. http://dx.doi.org/10.1007/3-540-46769-6_22.

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Greitāne, Inguna. "Probabilistic inductive inference of indices in enumerable classes of total recursive functions." In Analogical and Inductive Inference, 277–87. Berlin, Heidelberg: Springer Berlin Heidelberg, 1989. http://dx.doi.org/10.1007/3-540-51734-0_68.

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Freivalds, Rūsiņš, Dace Gobleja, Marek Karpinski, and Carl H. Smith. "Co-learnability and FIN-identifiability of enumerable classes of total recursive functions." In Lecture Notes in Computer Science, 100–105. Berlin, Heidelberg: Springer Berlin Heidelberg, 1994. http://dx.doi.org/10.1007/3-540-58520-6_57.

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Fernández, Maribel. "Recursive Functions." In Undergraduate Topics in Computer Science, 55–68. London: Springer London, 2009. http://dx.doi.org/10.1007/978-1-84882-434-8_4.

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Shen, A., and N. Vereshchagin. "Recursive functions." In The Student Mathematical Library, 139–57. Providence, Rhode Island: American Mathematical Society, 2002. http://dx.doi.org/10.1090/stml/019/11.

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Murawski, Roman. "Recursive Functions." In Recursive Functions and Metamathematics, 19–95. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-017-2866-9_2.

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Krantz, Steven G. "Recursive Functions." In Handbook of Logic and Proof Techniques for Computer Science, 85–94. Boston, MA: Birkhäuser Boston, 2002. http://dx.doi.org/10.1007/978-1-4612-0115-1_6.

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Conference papers on the topic "Classes of recursive functions"

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Mayra, Hannu, and Mauno Ronkko. "Functional Classes: Cost of Recursive Method Call in Java." In International Conference on Software Engineering Advances (ICSEA 2007). IEEE, 2007. http://dx.doi.org/10.1109/icsea.2007.35.

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Motato, Eliot, and Clark J. Radcliffe. "Networked Assembly of Nonlinear Physical System Models." In ASME 2007 International Mechanical Engineering Congress and Exposition. ASMEDC, 2007. http://dx.doi.org/10.1115/imece2007-41093.

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Engineering design is evolving into a global strategy that distributes model information through computer networks. This strategy requires companies to provide dynamic models of supplied physical components. Component models are transmitted through the Internet to a common location and then assembled to obtain a product dynamic model. Internet connection permitting, real-time, automated assembly of models requires four characteristics. Specifically, physical models must have a unique standard format, the exchange of model information must be executed in a single-query transmission, the models must describe only external behavior, and the assembly process must be recursive. The Modular Modeling Method (MMM) is an energy based model distribution and assembly algorithm that satisfies these four requirements. The MMM distributes and assembles linear and affine physical systems models using dynamic matrices. Though the MMM procedure can be used for a large class of systems, the dynamic matrices cannot be used to represent nonlinear behavior. A more general nonlinear model representation is required. This work is an extension of the MMM algorithm to assemble physical systems models characterized by analytic nonlinearities. This is a more general procedure that uses Volterra transfer functions to represent nonlinear behavior. Any analytic nonlinear system can be represented through a Volterra model. The reason why we use Volterra models instead ODEs is because Volterra models are only in function of input and output variables. This characteristic facilitates their use in an energy based model assembly method such as the MMM procedure. A procedure to assemble standard Volterra models using conservation energy principle is described. Even though there are extensive literature about gluing models, these techniques do not have all the characteristics needed by the MMM procedure. Using the approach proposed here, complex model assemblies can be executed recursively while hiding the topology and characteristics of their structural model subassemblies.

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Kneuss, Etienne, Ivan Kuraj, Viktor Kuncak, and Philippe Suter. "Synthesis modulo recursive functions." In SPLASH '13: Conference on Systems, Programming, and Applications: Software for Humanity. New York, NY, USA: ACM, 2013. http://dx.doi.org/10.1145/2509136.2509555.

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KVĚTOŇ, P., and V. KOUBEK. "FUNCTIONS PRESERVING CLASSES OF LANGUAGES." In Proceedings of the 4th International Conference. WORLD SCIENTIFIC, 2000. http://dx.doi.org/10.1142/9789812792464_0008.

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Chen, Yu-Fang, Bow-Yaw Wang, and Kai-Chun Yang. "Learning Summaries of Recursive Functions." In 2014 21st Asia-Pacific Software Engineering Conference (APSEC). IEEE, 2014. http://dx.doi.org/10.1109/apsec.2014.53.

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Ferizis, George, and Hossam Gindy. "Mapping Recursive Functions to Reconfigurable Hardware." In 2006 International Conference on Field Programmable Logic and Applications. IEEE, 2006. http://dx.doi.org/10.1109/fpl.2006.311226.

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Freivalds, Rūsiņš, Marek Karpinski, and Carl H. Smith. "Co-learning of total recursive functions." In the seventh annual conference. New York, New York, USA: ACM Press, 1994. http://dx.doi.org/10.1145/180139.181098.

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Jeffrey, D. J., and A. D. Rich. "Recursive integration of piecewise-continuous functions." In the 1998 international symposium. New York, New York, USA: ACM Press, 1998. http://dx.doi.org/10.1145/281508.281649.

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Vogt, A. "Should activation functions be affinely recursive?" In Proceedings of the IEEE-INNS-ENNS International Joint Conference on Neural Networks. IJCNN 2000. Neural Computing: New Challenges and Perspectives for the New Millennium. IEEE, 2000. http://dx.doi.org/10.1109/ijcnn.2000.857850.

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Draggiotis, Petros. "Recursive relations for multiparton splitting functions." In “Loops and Legs in Quantum Field Theory ” 11th DESY Workshop on Elementary Particle Physics. Trieste, Italy: Sissa Medialab, 2013. http://dx.doi.org/10.22323/1.151.0054.

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Reports on the topic "Classes of recursive functions"

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Kailath, Thomas. Recursive Analysis of Matrix Scattering Functions. Fort Belvoir, VA: Defense Technical Information Center, December 1993. http://dx.doi.org/10.21236/ada277264.

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Geisler-Moroder, David, Eleanor S. Lee, Gregory Ward, Bruno Bueno, Lars O. Grobe, Taoning Wang, Bertrand Deroisy, and Helen Rose Wilson. BSDF Generation Procedures for Daylighting Systems. IEA SHC Task 61, January 2021. http://dx.doi.org/10.18777/ieashc-task61-2021-0001.

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Abstract:

This white paper summarizes the current state of the art in the field of measurement and simulation characterization of daylighting systems by bidirectional scattering distribution functions (BSDFs) and provides recommendations broken down by classes of systems and use cases.

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