- 1.G. Bioul, M. Davio, and J.-P. Deschamps, "Minimization of ring-sum expansions of Boolean functions," Philips Res. Repts., Vol. 28, pp. 17-36, 1973.Google Scholar
- 2.R. E. Bryant, "Graph-based algorithms for Boolean function manipulation," IEEE Trans. Comput., Vol. C-35, No. 8, pp. 677-691, Aug. 1986. Google ScholarDigital Library
- 3.C.-H. Chang and B. J. Falkowski, "Flexible optimization of fixed polarity Reed-Muller expansions for multiple output completely and incompletely specified Boolean functions," Proc. Asia and South Pacific Design Automation Conference, pp. 335-340, Sept. 1995. Google ScholarDigital Library
- 4.C.-H. Chang and B. J. Falkowski, "Adaptive exact optimisation of minimally testable FPRM expansions," IEE Proceedings-Computers and Digital Techniques, Vol. 145, No. 6, pp. 385-394, Nov. 1998.Google ScholarCross Ref
- 5.E. M. Clarke, K. L. McMillan, X. Zhao, M. Fujita, and J. Yang, "Spectral transforms for large Boolean functions with applications to technology mapping," Proc. Design Automation Conference, pp. 54-60, June 1993. Google ScholarDigital Library
- 6.M. Davio, J.-P. Deschamps, and A. Thayse, Discrete and Switching Functions, McGraw-Hill International, 1978.Google Scholar
- 7.R. Drechsler, M. Theobald, and B. Becker, "Fast OFDD- based minimization of fixed polarity Reed-Muller expressions," IEEE Trans. Comput., Vol. C-45, No. 11, pp. 1294-1299, Nov. 1996. Google ScholarDigital Library
- 8.D. H. Green, "Reed-Muller expansions of incompletely specified functions," IEE Proceedings, Vol. 134, Pt. E, No. 5, pp. 228-236, Sept. 1987.Google Scholar
- 9.S. L. Hurst, D. M. Miller, and J. C. Muzio, Spectral Techniques in Digital Logic, Academic Press Inc., 1985. Google ScholarDigital Library
- 10.U. Kebschull and W. Rosenstiel, "Efficient graph-based computation and manipulation of functional decision diagrams," Proc. European Conference on Design Automation, pp. 278-282, Mar. 1993.Google Scholar
- 11.B. W. Kernighan and D. M. Ritchie, The C Programming Language, Second Edition, Prentice-Hall, 1988. Google ScholarDigital Library
- 12.P. K. Lui and J. C. Muzio, "Boolean matrix transforms for the minimization of modulo-2 canonical expressions," IEEE Trans. Comput., Vol. C-41, No. 3, pp. 342-347, Mar. 1992. Google ScholarDigital Library
- 13.L. McKenzie, A. E. A. Almaini, J. F. Miller, and P. Thomson, "Optimisation of Reed-Muller logic functions," International Journal of Electronics, Vol. 75, No. 3, pp. 451- 466, Sept. 1993.Google ScholarCross Ref
- 14.A. Sarabi and M. A. Perkowski, "Fast exact and quasiminimal minimization of highly testable fixed polarity AND/XOR canonical networks," Proc. Design Automation Conference, pp. 30-35, June 1992. Google ScholarDigital Library
- 15.T. Sasao, "AND-EXOR expressions and their optimization," in T. Sasao, ed., Logic Synthesis and Optimization, Kluwer Academic Publishers, 1993. Google ScholarDigital Library
- 16.T. Sasao, "Representations of logic functions using EXOR operators," in T. Sasao and M. Fujita, eds., Representations of Discrete Functions, Kluwer Academic Publishers, 1996.Google Scholar
- 17.T. Sasao and F. Izuhara, "Exact minimization of FPRMs using multi-terminal EXOR TDDs," in T. Sasao and M. Fujita, eds., Representations of Discrete Functions, Kluwer Academic Publishers, 1996.Google Scholar
- 18.T. Sasao, Switching Theory for Logic Synthesis, Kluwer Academic Publishers, 1999. Google ScholarDigital Library
- 19.F. Somenzi, CUDD: CU Decision Diagram Package, Release 2.3.0, University of Colorado at Boulder, 1998 (http://vlsi.colorado.edu/~fabio/).Google Scholar
- 20.A. Tran, "Graphical method for the conversion of minterms to Reed-Muller coefficients and the minimization of exclusive-OR switching functions," IEE Proceedings, Vol. 134, Pt. E, No. 2, pp. 93-99, Mar. 1987.Google Scholar
- 21.C. Tsai and M. Marek-Sadowska, "Minimisation of fixed-polarity AND/XOR canonical networks," IEE Proceedings-Computers and Digital Techniques, Vol. 141, No. 6, pp. 369-374, Nov. 1994.Google ScholarCross Ref
- 22.C. Tsai and M. Marek-Sadowska, "Generalized Reed- Muller forms as a tool to detect symmetries," IEEE Trans. Comput., Vol. 45, No. 1, pp. 33-40, Jan. 1996. Google ScholarDigital Library
- 23.C. Tsai and M. Marek-Sadowska, "Multilevel logic synthesis for arithmetic functions," Proc. 33rd Design Automation Conference, pp. 242-247, June 1996. Google ScholarDigital Library
- 24.C. Tsai and M. Marek-Sadowska, "Boolean functions classification via fixed polarity Reed-Muller forms," IEEE Trans. Comput., Vol. C-46, No. 2, pp. 173-186, Feb. 1997. Google ScholarDigital Library
- 25.D. Varma and E. A. Trachtenberg, "Computation of Reed-Muller expansions of incompletely specified Boolean functions from reduced representations," IEE Proceedings-E, Vol. 138, No. 2, pp. 85-92, Mar. 1991.Google Scholar
- 26.A. Zakrevskij, "Minimizing polynomial implementation of weakly specified logic functions and systems," Proc. 3rd International Workshop on Applications of the Reed-Muller Expansion in Circuit Design, pp. 157-166, Sept. 1997.Google Scholar
- 27.I. I. Zhegalkin, "The technique of calculation of statements in symbolic logic," Mathe. Sbornik, Vol. 34, pp. 9-28, 1927 (in Russian).Google Scholar
- 28.Z. Zilic and Z. G. Vranesic, "A multiple-valued Reed- Muller transform for incompletely specified functions," IEEE Trans. Comput., Vol. C-44, No. 8, pp. 1012-1020, Aug. 1995. Google ScholarDigital Library
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