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Remarks on Calculation of Autocorrelation on Finite Dyadic Groups by Local Transformations of Decision Diagrams

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Computer Aided Systems Theory – EUROCAST 2005 (EUROCAST 2005)

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Abstract

The paper considers calculation of autocorrelation functions on finite dyadic groups over decision diagrams. The methods exploit recursive structure of both autocorrelation matrices and decision diagrams. First, it is discussed calculation of the autocorrelation through the Wiener-Khinchin theorem implemented over decision diagrams. Then, it is proposed a method for calculation of separate autocorrelation coefficients over decision diagrams with permuted labels at the edges. For the case of restricted memory resources, a procedure with in-place calculations over the decision diagram for the function processed has been defined.

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References

  1. Agaian, S., Astola, J., Egiazarian, K.: Binary Polynomial Transforms and Nonlinear Digital Filters. Marcel Dekker, New York (1995)

    Google Scholar 

  2. Bracewell, R.: The Autocorrelation Function. In: The Fourier Transform and Its Applications, 3rd edn., pp. 40–45. McGraw-Hill, New York (1999)

    Google Scholar 

  3. Bryant, R.E.: Graph-based algorithms for Boolean functions manipulation. IEEE Trans. Comput. C-35(8), 667–691 (1986)

    Article  Google Scholar 

  4. Clarke, E., Millan, M.M.C., Zhao, K.L., Fujita, X.,, M.: Spectral transforms for extremely large Boolean functions. In: Kebschull, U., Schubert, E., Rosenstiel, W. (eds.) Proc. IFIP WG 10.5 Workshop on Applications of the Reed-Muller Expression in circuit Design, Workshop Reed-Muller 1993, Hamburg, Germany, September 16-17, pp. 86–90 (1993)

    Google Scholar 

  5. Falkowski, B.J., Chang, C.H.: Properties and methods of calculating generalized arithmetic and adding transforms. IEE Proc. Circuits, Devices and Systems 144(5), 249–258 (1997)

    Article  Google Scholar 

  6. Karpovsky, M.G.: Finite Orthogonal Series in the Design of Digital Devices. John Wiley, Chichester (1976)

    MATH  Google Scholar 

  7. Karpovsky, M.G. (ed.): Spectral Techniques and Fault Detection, pp. 35–90. Academic Press, London (1985)

    MATH  Google Scholar 

  8. Karpovsky, M.G., Moskalev, E.S.: Utilization of autocorrelation characteristics for the realization of systems of logical functions. Avtomatika i Telmekhanika 2, 83–90 (1970); English translation Automatic and Remote Control 31, 342–350 (1970)

    Google Scholar 

  9. Karpovsky, M.G., Stanković, R.S., Astola, J.T.: Spectral techniques for design and testing of computer hardware. In: Proc. Int. Worksop on Spectral Techniques in Logic Design, SPECLOG 2000, Tampere, Finland, June 2-3, pp. 1–34 (2000)

    Google Scholar 

  10. Meinel, C., Somenzi, F., Tehobald, T.: Linear shifting of decision diagrams and its application in synthesis. IEEE Trans. CAD 19(5), 521–533 (2000)

    Google Scholar 

  11. Pichler, F.: Walsh functions and linear system theory. In: Proc. Applic. Walsh Functions, Washington, D.C., pp. 175–182 (1970)

    Google Scholar 

  12. Pichler, F.: Some Aspects of a Theory of Correlation with respect to Walsh Harmonic Analysis, Techn. Report. Dept. of Electrical Engineering, University of Maryland, Washington, DC, Report R-70-11 (August 1970)

    Google Scholar 

  13. Pichler, F.: Walsh-Fourier Synthese optimaler Filter, AEÜ, Band 24, Heft 7/8, 350–360 (1970)

    Google Scholar 

  14. Pichler, F.: Realizations of Prigogine’s Λ-transform by dyadic convolution. In: Trappl, R., Horn, W. (eds.) Austrian Society for Cybernetic Studies (1992) ISBN 385206127X

    Google Scholar 

  15. Rice, J.E.: Autocorrelation Cefficients in Representation and Classification of Switching Functions, Ph.D. Disertation, University of Victoria, Victoria, B.C., Canada (2003)

    Google Scholar 

  16. Rice, J.E., Muzio, J.C.: Methods for calculating autocorrelation coefficients. In: Proc. 4th Int. Workshop on Boolean Problems (IWSBP 2000), pp. 69–76 (2000)

    Google Scholar 

  17. Rice, J.E., Muzio, J.C.: Use of autocorrelation function in the classification of switching functions. In: Euromicro Symposium on Digital System Design, pp. 244–251 (2002)

    Google Scholar 

  18. Rice, J.E., Muzio, J.C.: Properties of autocorrelation coefficients. In: Proc. IEEE Pacific Rim Conf. on Comunications, Computers and Signal Processing (2003)

    Google Scholar 

  19. Rice, J.E., Muzio, J.C.: On the use of autocorrelation coefficients in the identification of three-level decompositions. In: Proc. PAC 2003, pp. 577–580 (2003)

    Google Scholar 

  20. Rice, J.E., Muzio, J.C.: On the use of autocorrelation coefficients in the identification of three-level decompositions. In: Proc. Int. Workshop on Logic Synthesis, IWLS 2003 (2003)

    Google Scholar 

  21. Rice, J., Serra, M., Muzio, J.C.: The use of autocorrelation coefficients for variable ordering for ROBDDs. In: Proc. 4th Int. Workshop on Applications of Reed-Muller Expansion in Circuit Design, Victoria, Canada, August 20-21, pp. 185–196 (1999)

    Google Scholar 

  22. Sasao, T., Fujita, M. (eds.): Representations of Discrete Functions. Kluwer, Dordrecht (1996)

    MATH  Google Scholar 

  23. Stanković, R.S., Astola, J.T.: Spectral Interpretation of Decision Diagrams. Springer, Heidelberg (2003)

    MATH  Google Scholar 

  24. Stanković, R.S., Sasao, T., Moraga, C.: Spectral transform decision diagrams. In: Sasao, T., Fujita, M. (eds.) Representations of Discrete Functions, pp. 55–92. Kluwer Academic Publishers, Dordrecht (1996)

    Google Scholar 

  25. Tomczuk, R.: Autocorrelation and Decomposition Methods in Combinational Logic Design, PhD thesis, University of Victoria (1996)

    Google Scholar 

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Stanković, R.S., Karpovsky, M.G. (2005). Remarks on Calculation of Autocorrelation on Finite Dyadic Groups by Local Transformations of Decision Diagrams. In: Moreno Díaz, R., Pichler, F., Quesada Arencibia, A. (eds) Computer Aided Systems Theory – EUROCAST 2005. EUROCAST 2005. Lecture Notes in Computer Science, vol 3643. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11556985_40

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  • DOI: https://doi.org/10.1007/11556985_40

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-29002-5

  • Online ISBN: 978-3-540-31829-3

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