Abstract
Two-level logic minimization is a central problem in logic synthesis, and has applications in reliability analysis and automated reasoning. This paper represents a method of minimizing Boolean sum of products function with binary decision diagram and with disjoint sum of product minimization. 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. The application of Binary Decision Diagrams (BDDs) as an efficient approach for the minimization of Disjoint Sums-of-Products (DSOPs). DSOPs are a starting point for several applications.
The use of BDDs has the advantage of an implicit representation of terms. Due to this scheme the algorithm is faster than techniques working on explicit representations and the application to large circuits that could not be handled so far becomes possible. Theoretical studies on the influence of the BDDs to the search space are carried out. In experiments the proposed technique is compared to others. The results with respect to the size of the resulting DSOP are as good or better as those of the other techniques.
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References
Yang, C., Ciesielski, M.: BDD-Based Logic Optimization System. IEEE Transactions on Computer Aided Design of Integrated Circuits and Systems 21(7), 866–876 (2002)
Popel, D.V.: Towards Efficient Calculation of Informationmeasures for Reordering of Binary Decision Diagrams. Computing Research Repository - CORR, cs.AR/0207 (2002)
Knuth, D.E.: The Art of Computer Programming, vol. 4
Swamy, G.M.: An Exact Logic Minimizer Using Implicit Binary Decision Diagram Based Methods. In: ICCAD 1994 Proceedings of the 1994 IEEE/ACM International Conference on Computer-Aided Design (1994)
Fey, G., Drechsler, R.: Utilizing BDDs for Disjoint SOP Minimization. In: 45th IEEE International Midwest Symposium on Circuits and Systems (2002)
Raidl, G.R., Cagnoni, S., Branke, J., Corne, D.W., Drechsler, R., Jin, Y., Johnson, C.G., Machado, P., Marchiori, E., Rothlauf, F., Smith, G.D., Squillero, G. (eds.): EvoWorkshops 2004. LNCS, vol. 3005. Springer, Heidelberg (2004)
Andersen, H.R.: An Introduction to Binary Decision Diagrams. Lecture Notes, Technical University of Denmark (October 1997)
Jain, J., Bitner, J., Moundanos, D., Abraham, J.A., Fussell, D.S.: A new scheme to compute variable orders for binary decision diagrams. In: Proceedings of the Fourth Great Lakes Symposium on, Design Automation of High Performance VLSI Systems, GLSV 1994, March 4-5, pp. 105–108 (1994)
Hilgemeier, M., Drechsler, N., Drechsler, R.: Minimizing the number of one-paths in BDDs by an evolutionary algorithm. In: Congress on Evolutionary Computation (2003)
Nosrati, M., Hariri, M.: An Algorithm for Minimizing of Boolean Functions Based on Graph DS. World Applied Programming 1(3), 209–214 (2011)
Coudert, O.: On solving Covering Problems. In: Proc. of 33rd DAC, Las Vegas (June 1996)
Brayton, R.K.: Logic minimization algorithms for VLSI synthesis
Bryant, R.E.: Graph-based algorithms for Boolean function manipulation. IEEE Transactions on Computers C-35-8, 677–691 (1986)
Bryant, R.E.: Symbolic Boolean Manipulation with Ordered Binary-Decision Diagrams. ACM Computing Surveys (1992)
Bryant, R.E.: Binary decision diagrams and beyond: Enabeling techniques for formal verification. In: Int’l Conf. on CAD, pp. 236–243 (1995)
Drechsler, R., Becker, B.: Binary Decision Diagrams – Theory and Implementation. Kluwer Academic Publishers (1998)
Kohavi, Z.: Switching and Finite Automata Theory
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© 2012 ICST Institute for Computer Science, Social Informatics and Telecommunications Engineering
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Sensarma, D., Banerjee, S., Basuli, K., Naskar, S., Sarma, S.S. (2012). Minimizing Boolean Sum of Products Functions Using Binary Decision Diagram. In: Meghanathan, N., Chaki, N., Nagamalai, D. (eds) Advances in Computer Science and Information Technology. Computer Science and Information Technology. CCSIT 2012. Lecture Notes of the Institute for Computer Sciences, Social Informatics and Telecommunications Engineering, vol 86. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-27317-9_5
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