Abstract
Recently, an approach has been presented to minimize Disjoint Sum-of-Products (DSOPs) based on Binary Decision Diagrams (BDDs). Due to the symbolic representation of cubes for large problem instances, the method is orders of magnitude faster than previous enumerative techniques. But the quality of the approach largely depends on the variable ordering of the underlying BDD.
This paper presents an Evolutionary Algorithm (EA) to optimize the DSOP representation of a given Boolean function. The EA is used to find an optimized variable ordering for the BDD representation. Then the DSOP is derived from the optimized BDD using structural and symbolic techniques. Experiments are performed to adjust the parameters of the EA. Experimental results are given to demonstrate the efficiency of the approach.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. on Comp. 35(8), 677–691 (1986)
Bryant, R.E.: Binary decision diagrams and beyond: Enabling techniques for formal verification. In: Int’l Conf. on CAD, pp. 236–243 (1995)
Davis, L.: Applying adaptive algorithms to epistatic domains. In: Proceedings of IJCAI, pp. 162–164 (1985)
Davis, L.: Handbook of Genetic Algorithms. van Nostrand Reinhold, New York (1991)
Drechsler, R.: Evolutionary Algorithms for VLSI CAD. Kluwer Academic Publishers, Dordrecht (1998)
Drechsler, R., Becker, B., Göckel, N.: A genetic algorithm for variable ordering of OBDDs. In: IEE Proceedings, vol. 143(6), pp. 364–368 (1996)
Falkowski, B.J.: Calculation of rademacher-walsh spectral coefficients for systems of completely and incompletely specified boolean functions. In: IEEE Proceedings on Circuits, pp. 1698–1701 (1993)
Falkowski, B.J., Chang, C.-H.: Paired haar spectra computation through operations on disjoint cubes. In: IEEE Proceedings on Circuits, Devices and Systems, pp. 117–123 (1999)
Falkowski, B.J., Schäfer, I., Chang, C.-H.: An effective computer algorithm for the calculation of disjoint cube representation of boolean functions. In: Midwest Symposium on Circuits and Systems, pp. 1308–1311 (1993)
Ferrandi, F., Macii, A., Macii, E., Poncino, M., Scarsi, R., Somenzi, F.: Symbolic algorithms for layout-oriented synthesis of pass transistor logic circuits. In: Int’l Conf. on CAD, pp. 235–241 (1998)
Fey, G., Drechsler, R.: A hybrid approach combining symbolic and structural techniques for disjoint SOP minimization. In: Workshop on Synthesis And System Integration of Mixed Information technologies (SASIMI), pp. 54–60 (2003)
Göckel, N., Drechsler, R., Becker, B.: GAME: A software environment for using genetic algorithms in circuit design. Applications of Computer Systems, 240–247 (1997)
Goldberg, D.E., Lingle, R.: Alleles, loci, and the traveling salesman problem. In: Int’l Conference on Genetic Algorithms, pp. 154–159 (1985)
Hilgemeier, M., Drechsler, N., Drechsler, R.: Minimizing the number of one-paths in BDDs by an evolutionary algorithm. In: Congress on Evolutionary Computation, pp. 1724–1731 (2003)
Kropf, T.: Introduction to Formal Hardware Verification. Springer, Heidelberg (1999)
Lai, Y.-T., Sastry, S., Pedram, M.: Boolean matching using binary decision diagrams with applications to logic synthesis and verification. In: Int’l Conf. on CAD, pp. 452–458 (1992)
Mishchenko, A., Perkowski, M.: Fast heuristic minimization of exclusive-sumsof- products. In: Int’l Workshop on Applications of the Reed-Muller Expansion in Circuit Design, pp. 242–250 (2001)
Oliver, I.M., Smith, D.J., Holland, J.R.C.: A study of permutation crossover operators on the traveling salesman problem. In: Int’l Conference on Genetic Algorithms, pp. 224–230 (1987)
Rudell, R.: Dynamic variable ordering for ordered binary decision diagrams. In: Int’l Conf. on CAD, pp. 42–47 (1993)
Sasao, T.: EXMIN2: A simplification algorithm for Exclusive-OR-Sum-of products expressions for multiple-valued-input two-valued-output functions. IEEE Trans. on CAD 12, 621–632 (1993)
Shivakumaraiah, L., Thornton, M.: Computation of disjoint cube representations using a maximal binate variable heuristic. In: Southeastern Symposium on System Theory, pp. 417–421 (2002)
Thornton, M., Drechsler, R., Miller, D.M.: Spectral Techniques in VLSI CAD. Kluwer Academic Publishers, Dordrecht (2001)
Whitley, D., Starkweather, T., Fuquay, D.: Scheduling problems and traveling salesman: The genetic edge recombination operator. In: Int’l Conference on Genetic Algorithms, pp. 133–140 (1989)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Drechsler, N., Hilgemeier, M., Fey, G., Drechsler, R. (2004). Disjoint Sum of Product Minimization by Evolutionary Algorithms. In: Raidl, G.R., et al. Applications of Evolutionary Computing. EvoWorkshops 2004. Lecture Notes in Computer Science, vol 3005. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24653-4_21
Download citation
DOI: https://doi.org/10.1007/978-3-540-24653-4_21
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-21378-9
Online ISBN: 978-3-540-24653-4
eBook Packages: Springer Book Archive