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Application of Indexed Partition Calculus in Logic Synthesis of Boolean Functions for FPGAs

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Functional decomposition of Boolean functions specified by cubes proved to be very efficient. Most popular decomposition methods are based on blanket calculus. However computation complexity of blanket manipulations strongly depends on number of function's variables, which prevents them from being used for large functions of many input and output variables. In this paper a new concept of indexed partition is proposed and basic operations on indexed partitions are defined. Application of this concept to logic synthesis based on functional decomposition is also discussed. The experimental results show that algorithms based on new concept are able to deliver good quality solutions even for large functions and does it many times faster than the algorithms based on blanket calculus.
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  • Institute of Telecommunications, Warsaw University of Technology, Nowowiejska 15/19, 00-665 Warsaw, Poland, rawski@tele.pw.edu.pl
Bibliografia
  • [1] J. A. Brzozowski and T. Łuba, “Decomposition of Boolean Functions Specified by Cubes,” Journal of Multiple-Valued Logic and Soft Computing, vol. 9, pp. 377–417, 2003.
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  • [10] H. Selvaraj, M. Nowicka, and T. Łuba, “Performance Oriented Decomposition Strategies for FPGA Based Technology Mapping,” in International Conference VLSI for Signal Processing, Chennai, India, 1998.
  • [11] M. Rawski, L. Jóźwiak, and T. Łuba, “Functional Decomposition with an Efficient Input Support Selection for Sub-Functions Based on Information Relationship Measures,” Journal of Systems Architecture, vol. 47, no. 2, pp. 137–155, February 2001.
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  • [14] A. Chojnacki and L. Jóźwiak, “An Effective and Efficient Method for Functional Decomposition of Boolean Functions Based on Information Relationships Measures,” in Design and Diagnostics of Electronic Circuits and Systems DDECS'2000, Smolenice, Slovakia, April 2000.
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  • [20] M. Nowicka, T. Łuba, and M. Rawski, “FPGA-Based Decomposition of Boolean Functions, Algorithms and Implementation,” Advanced Computer Systems, pp. 502–509, 1999.
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  • [22] M. Rawski, Evolutionary Algorithms. Intech, 2011, ch. Evolutionary Algorithms in Decomposition-Based Logic Synthesis.
  • [23] M. Rawski, H. Selvara, T. Łuba, and P. Szotkowski, “Multilevel Synthesis of Finite State Machines Based on Symbolic Functional Decomposition,” International Journal of Computational Intelligence and Applications, vol. 6, no. 2, pp. 257–271, June 2006, imperial College Press.
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  • [25] J. Lewandowski, M. Rawski, and H. Rybiński, “Application of Parallel Decomposition for Creation of Reduced Feed-Forward Neural Networks,” in Proceedings of the International Conference, Rough Sets and Intelligent Systems Paradigms. Warsaw, Poland: Springer, 28-30 June 2007, pp. 564–573, lecture Notes in Artificial Intelligence, Subseries of Lecture Notes in Computer Science.
  • [26] H. Selvaraj, P. Sapiecha, and T. Łuba, “Functional Decomposition and Its Applications in Machine Learning and Neural Networks,” International Journal of Computational Intelligence and Applications, vol. 1, no. 3, pp. 259–271, 2001.
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Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-BWA0-0049-0035
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