
This Article  
 
Share  
Bibliographic References  
Add to:  
Digg Furl Spurl Blink Simpy Del.icio.us Y!MyWeb  
Search  
 
ASCII Text  x  
Mark G. Karpovsky, Radomir S. Stankovc, Jaakko T. Astola, "Reduction of Sizes of Decision Diagrams by Autocorrelation Functions," IEEE Transactions on Computers, vol. 52, no. 5, pp. 592606, May, 2003.  
BibTex  x  
@article{ 10.1109/TC.2003.1197126, author = {Mark G. Karpovsky and Radomir S. Stankovc and Jaakko T. Astola}, title = {Reduction of Sizes of Decision Diagrams by Autocorrelation Functions}, journal ={IEEE Transactions on Computers}, volume = {52}, number = {5}, issn = {00189340}, year = {2003}, pages = {592606}, doi = {http://doi.ieeecomputersociety.org/10.1109/TC.2003.1197126}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Reduction of Sizes of Decision Diagrams by Autocorrelation Functions IS  5 SN  00189340 SP592 EP606 EPD  592606 A1  Mark G. Karpovsky, A1  Radomir S. Stankovc, A1  Jaakko T. Astola, PY  2003 KW  Logic synthesis KW  spectral techniques KW  decision diagrams KW  linear transforms KW  autocorrelation functions. VL  52 JA  IEEE Transactions on Computers ER   
Abstract—This paper discusses optimization of decisions diagrams (DDs) by total autocorrelation functions. We present an efficient algorithm for construction of Linearly Transformed Binary Decision Diagrams (LTBDDs) and Linearly transformed multiterminal BDDs (LTMTBDDs) for systems of Boolean functions, based on linearization of these functions by the corresponding autocorrelation functions. Then, we present a method for reduction of sizes of DDs by a levelbylevel reduction of the width of DDs using the total autocorrelation functions. The approach provides for a simple procedure for minimization of LTBDDs and LTMTBDDs and upper bounds on their sizes. Experimental results for benchmarks illustrate that the proposed method on average is very efficient.
[1] S. Agaian, J. Astola, and K. Egiazarian, Binary Polynomial Transforms and Nonlinear Digital Filters. Marcel Dekker, 1995.
[2] J. Bern, C. Meinel, and A. Slobodova, “Efficient OBDDBased Manipulation in CAD Beyond Current Limits,” Proc. 32nd Design Automation Conf., pp. 408413, 1995.
[3] B. Bollig and I. Wegener, “Improving the Variable Ordering of OBDDs is NPComplete,” IEEE Trans. Computers, vol. 45, no. 9, pp. 9931002, 1996.
[4] R.E. Bryant, “GraphBased Algorithms for Boolean Functions Manipulation,” IEEE Trans. Computers, vol. 35, no. 8, pp. 667691, 1986.
[5] E.M. Clarke, K.L. McMillan, X. Zhao, and M. Fujita, “Spectral Transforms for Extremely Large Boolean Functions,” Proc. IFIP WG 10.5 Workshop on Applications of the ReedMuller Expression in Circuit Design, U. Kebschull, E. Schubert, and W. Rosenstiel, eds., pp. 8690, Sept. 1993.
[6] R. Drechsler and B. Becker, Binary Decision Diagrams, Theory and Impementation, Kluwer Academic Publishers, 1998.
[7] M. Fujita, Y. Kukimoto, and R.K. Brayton, “BDD Minimization by Truth Table Permutation,” Proc. Int'l Symp. Circuits and Systems, vol. 4, pp. 596599, May 1996.
[8] M. Fujita, Y. Matsunaga, and T. Kakuda, "On variable Ordering of Binary Decision Diagrams for the Application of MultiLevel Logic Synthesis," Proc. European Design Automation Conf., pp. 5054, 1991.
[9] M. Fujita, J.C.Y. Yang, M. Clarke, X. Zhao, and P. McGeer, “Fast Spectrum Computation for Logic Functions Using Binary Decision Diagrams,” Proc. Int'l Symp. ComputerAided Surgery (ISCAS '94), pp. 275278, 1994.
[10] W. Günther and R. Drechsler, “BDD Minimization by Linear Transforms,” Advanced Computer Systems, pp. 525532, 1998.
[11] W. Günther and R. Drechsler, “Efficient Manipulation Algorithms for Linearly Transformed BDDs,” Proc. Fourth Int'l Workshop Applications of ReedMuller Expansion in Circuit Design, pp. 225232, May 1999.
[12] W. Günther and R. Drechsler, “Minimization of BDDs Using Linear Transformations Based on Evolutionary Techniques,” Proc. Int'l Symp. Circuit and Systems, 1999.
[13] M.G. Karpovsky, Finite Orthogonal Series in the Design of Digital Devices. John Wiley, 1976.
[14] M.G. Karpovsky and E.S. Moskalev, “Utilization of Autocorrelation Characteristics for the Realization of Systems of Logical Functions,” Avtomatika i Telmekhanika, no. 2, pp. 8390, 1970.
[15] Spectral Techniques and Fault Detection. M.G. Karpovsky, ed., pp. 3590, Academic Press, 1985.
[16] M.G. Karpovsky, R.S. Stanković, and J.T. Astola, “Spectral Techniques for Design and Testing of Computer Hardware,” Proc. Int'l Workshop Spectral Techniques in Logic Design, pp. 134, June 2000.
[17] R.J. Lechner and A. Moezzi, “Synthesis of Encoded PLAs,” Spectral Techniques and Fault Detection, 1985.
[18] C. Meinel, F. Somenzi, and T. Theobald, “Linear Sifting of Decision Diagrams,” Proc. Design Automation Conf., pp. 202207, 1997.
[19] C. Meinel, F. Somenzi, and T. Theobald, Linear Sifting of Decision Diagrams and Its Application in Synthesis IEEE Trans. Computer Automated Design, vol. 19, no. 5, pp. 521533, 2000.
[20] D. Milošević, R.S. Stanković, and C. Moraga, “Calculation of Dyadic Autocorrelation throguh Decision Diagrams,” Proc. Int'l Workshop Computational Intelligence and Information Technologies, pp. 129134, June 2001.
[21] S. Minato, “GraphBased Representations of Discrete Functions,” Representations of Discrete Functions, pp. 128, 1996.
[22] S. Panda and F. Somenzi, “Who Are the Variables in Your Neigborhood,” Proc. IEEE Int'l Conf. ComputerAided Design, pp. 7477, 1995.
[23] S. Panda, F. Somenzi, and B. Plessier, "Symmetry Detection and Dynamic Variable Ordering of Decision Diagrams," Proc. ICCAD94, pp. 628631, 1994.
[24] J. Rice, M. Serra, and J.C. Muzio, “The use of Autocorrelation Coefficients for Variable Ordering for ROBDDs,” Proc. Fourth Int'l Workshop Applications of ReedMuller Expansion in Circuit Design, pp. 185196, Aug. 1999.
[25] R. Rudell, "Dynamic Variable Ordering for Ordered Binary Decision Diagrams," Proc. ICCAD93, pp. 4247, 1993.
[26] T. Sasao, Switching Theory for Logic Synthesis. Kluwer Academic Publishers, 1999.
[27] Representations of Discrete Functions, T. Sasao and M. Fujita, eds., Kluwer, 1996.
[28] M. Sauerhoff, I. Wegener, and R. Werchner, “Optimal Ordered Binary Decision Diagrams for ReadOnce Formulas,” Discrete Applied Math., vol. 103, pp. 237258, 2000.
[29] D. Sieling, “On the Existence of Polynomial Time Approximation Schemes for OBDD Minimization,” Proc. Symp. Theoretical Aspects of Computer Science, vol. 1373, pp. 205215, 1998.
[30] F. Somenzi, CUDD—Colorado Univ. Decision Diagram Package, 1996.
[31] R.S. Stanković, Spectral Transform Decision Diagrams in Simple Questions and Simple Answers. Belgrade: Nauka, 1998.
[32] R.S. Stanković, “Some Remarks on Basic Characteristics of Decision Diagrams,” Proc. Fourth Int'l Workshop Applications of ReedMuller Expansion in Circuit Design, pp. 139146, Aug. 1999.
[33] R.S. Stanković, M. Bhattacharaya, and J.T. Astola, “Calulation of Dyadic Autocorrelation through Decision Diagrams,” Proc. European Conf. Circuit Theory and Design, pp. 337340, Aug. 2001.
[34] R.S. Stanković and T. Sasao, “Decision Diagrams for Representation of Discrete Functions: Uniform Interpretation and Classification,” Proc. Asia and South Pacific Design Automation Conf., Feb. 1998.
[35] R.S. Stanković, T. Sasao, and C. Moraga, “Spectral Transform Decision Diagrams,” Representations of Discrete Functions, pp. 5592, 1996.
[36] E.A. Trachtenberg, “SVD of Frobenius Matrices for Approximate and Multiobjective Signal Processing Tasks,” SVD and Signal Processing, E.F. Derettere, ed., pp. 331345, Elsevier, 1988.
[37] I. Wegener, “Worst Case Examples for Operations over OBDDs,” Information Processing Letters, no. 74, pp. 9194, 2000.