Abstract
A theoretical approach to a novel design method for special purpose processors for computable integral transforms and related operations is presented. The method is based on algebraic processor models and Type-2 Theory of Effectivity and aims for specification formalization and calculation reliability together with implementation feasibility. The convolution operation is presented as a case of study.
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Andrews, D., Niehaus, D., Jidin, R., Finley, M., Peck, W., Frisbie, M., Ortiz, J., Komp, E., Ashenden, P.: Programming Models for Hybrid FPGA-CPU Computational Components: A Missing Link. IEEE Micro 24, 42–53 (2004)
Ercegovac, M.D., Lang, T.: Digital Arithmetic. Morgan Kaufmann, San Francisco (2004)
Fox, A.C.J.: Formal specification and verification of ARM6. In: Basin, D., Wolff, B. (eds.) TPHOLs 2003. LNCS, vol. 2758, pp. 25–40. Springer, Heidelberg (2003)
Fox, A.C.J., Harman, N.A.: Algebraic Models of Correctness for Abstract Pipelines. The Journal of Algebraic and Logic Programming 57, 71–107 (2003)
Gowland, P., Lester, D.: A Survey of Exact Arithmetic Implementations. In: Blank, J., Brattka, V., Hertling, P. (eds.) CCA 2000. LNCS, vol. 2064, pp. 30–47. Springer, Heidelberg (2001)
Harman, N.A., Tucker, J.V.: Algebraic models of microprocessors: the verification of a simple computer. In: Proc. 2nd IMA Conference, pp. 135–170 (1997)
Klunkle, D.: Type-2 computability on spaces of integrable functions. Math. Log. Quart. 50, 417–430 (2004)
Lynch, T., Schulte, M.: A High Radix On-line Arithmetic for Credible and Accurate Computing. Journal of UCS 1, 439–453 (1995)
McEvoy, K., Tucker, J.V.: Theoretical Foundations of VLSI Design. Cambridge Tracts in Theoretical Computer Science, vol. 10 (1990)
Möller, B., Tucker, J.V. (eds.): NADA 1997. LNCS, vol. 1546. Springer, Heidelberg (1998)
Weihrauch, K.: Computable Analysis. Springer, Heidelberg (2000)
Zhong, N., Weihrauch, K.: Computability Theory of Generalized Functions. Journal of the ACM 50, 469–505 (2003)
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de Miguel Casado, G., Chamizo, J.M.G. (2006). The Role of Algebraic Models and Type-2 Theory of Effectivity in Special Purpose Processor Design. In: Beckmann, A., Berger, U., Löwe, B., Tucker, J.V. (eds) Logical Approaches to Computational Barriers. CiE 2006. Lecture Notes in Computer Science, vol 3988. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11780342_15
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DOI: https://doi.org/10.1007/11780342_15
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-35466-6
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