Complexity of two-level logic minimization

IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems

Volumn 25, Issue 7, 2006, Pages 1230-1246

  Umans, Christopher ^b   Villa, Tiziano ^c,d   Sangiovanni Vincentelli, Alberto L ^{a,d,e,f,g,h,i}  

^a IEEE   (Italy)

^b CALIFORNIA INSTITUTE OF TECHNOLOGY   (United States)

^c UNIVERSITY OF UDINE   (Italy)

^d PARADES   (Italy)

^e UNIVERSITY OF CALIFORNIA   (United States)

^f University of California ^*  (Italy)

^g Accent an ST Microelectronics Cadence   (United States)

^h GENERAL MOTORS CORPORATION   (United States)

ⁱ National Academy of Engineering   (Italy)

Author keywords

Computational complexity; Logic design; Logic minimization; Two level logic

Indexed keywords

LOGIC MINIMIZATION; LOGIC SYNTHESIS; REAL-WORLD IMPACT; TWO-LEVEL LOGIC;

CLASSIFICATION (OF INFORMATION); COMPUTATIONAL COMPLEXITY; COMPUTER AIDED DESIGN; OPTIMIZATION; TERMINOLOGY;

LOGIC DESIGN;

EID: 33744764298     PISSN: 02780070     EISSN: None     Source Type: Journal    
DOI: 10.1109/TCAD.2005.855944     Document Type: Article

References (34)

1. E. Allender, L. Hellerstein, P. M. McCabe, T. Pitassi, and M. Saks, "Minimizing DNF formulas and AC0 circuits given a truth table," ECCC Tech. Rep. TR05-126, 2005.
2. D. Bovet and P. Crescenzi, Introduction to the Theory of Complexity. Englewood Cliffs, NJ: Prentice-Hall, 1994.
3. R. Brayton, G. Hachtel, C. McMullen, and A. Sangiovanni-Vincentelli, Logic Minimization Algorithms for VLSI Synthesis, Boston, MA: Kluwer, 1984.
4. R. Brayton, A. Sangiovanni-Vincentelli, and G. Hachtel, "Multi-level logic synthesis," Proc. IEEE, vol. 78, no. 2, pp. 264-300, Feb. 1990.
5. V. Ciriani, "Synthesis of SPP three-level logic networks using affine spaces," IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 22, no. 10, pp. 1310-1323, Oct. 2003.
6. O. Coudert, "Two-level logic minimization: An overview," Integration, vol. 17, no. 2, pp. 97-140, Oct. 1994.
7. S. L. A. Czort, "The complexity of minimizing disjunctive normal form formulas," M.S. thesis, Dept. Comput. Sci., Univ. Aarhus, Aarhus, Denmark, 1999.
8. M. Gao, J.-H. Jiang, Y. Jiang, Y. Li, A. Mishchenko, S. Sinha, T. Villa, and R. Brayton, "Optimization of multi-valued multi-level networks," in Proc. Int. Symp. Multiple-Valued Logic, Sendai, Japan, May 2002, pp. 168-177.
9. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness. San Francisco, CA: Freeman, 1979.
10. J. Gimpel, "A method of producing a Boolean function having an arbitrarily prescribed prime implicant table," IRE Trans. Electron. Comput., vol. EC-14, no. 6, pp. 485-488, Jun. 1965.
11. K. Hayase and H. Imai, "OBDDs of a monotone function and of its prime implicants," in Proc. 7th Int. Symp. Algorithms and Computation (ISAAC), Osaka, Japan, 1178, Lecture Notes in Computer Science. New York: Springer-Verlag, 1996, pp. 136-145.
12. V. Kabanets and J.-Y. Cai, "Circuit minimization problem," in Proc. 32nd Annu. ACM Symp. Theory Computing (STOC), Portland, OR, 2000, pp. 73-79.
13. R. Karp, "Reducibility among combinatorial problems," in Complexity of Computer Computations, R. E. Miller and J. W. Thatcher, Eds. New York: Plenum, 1972, pp. 85-103.
14. K. Keutzer and D. Richards, "Computational complexity of logic synthesis and optimization," presented at the Int. Workshop Logic Synthesis, Research Triangle Park, NC, May 1989.
15. W. J. Masek, "Some NP-complete set covering problems," M.S. thesis, MIT Lab. Comput. Sci., Massachusetts Inst. Technol., Cambridge, May 1978.
16. E. McCluskey, "Minimization of Boolean functions," Bell Lab. Tech. J., vol. 35, no. 6, pp. 1417-1444, Nov. 1956.
17. P. McGeer, J. Sanghavi, R. Brayton, and A. Sangiovanni-Vincentelli, "ESPRESSO-SIGNATURE: A new exact minimizer for logic functions," IEEE Trans. Very Large Scale Integr. (VLSI) Syst., vol. 1, no. 4, pp. 432440, Dec. 1993.
18. F. Mo and R. Brayton, "PLA-based regular structures and their synthesis," IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 22, no. 6, pp. 723-729, Jun. 2003.
19. C. Papadimitriou, Computational Complexity. Reading, MA: Addison-Wesley, 1994.
20. W. Paul, "Boolean minimum polynomials and covering problems," (in German) Acta Inform., vol. 4, no. 4, pp. 321-336, 1975, Transl.: Boolesche Minimalpolynome and Ueberdeckungsprobleme.
21. R. Rudell and A. Sangiovanni-Vincentelli, "Multiple-valued minimization for PLA optimization," IEEE Trans. Comput.-Aided Des. Integr, Circuits Syst., vol. CAD-6, no. 5, pp. 727-750, Sep. 1987.
22. S. Sapra, M. Theobald, and E. M. Clarke, "Sat-based algorithms for logic minimization," in Proc. Int. Conf. Computer Design, San Jose, CA, Oct. 2003, p. 510.
23. M. Schaefer and C. Umans, "Completeness in the polynomial-time hierarchy: A compendium," SIGACT News, vol. 33, no. 3, pp. 32-49, Sep. 2002.
24. _, "Completeness in the polynomial-time hierarchy: Part II," SIGACT News, vol. 33, no. 4, pp. 22-36, Dec. 2002
25. D. Sieling, "The complexity of minimizing and learning OBDDs and FBDDs," Discrete Appl. Math., vol. 122, no. 1-3, pp. 263-282, Oct. 2002.
26. L. J. Stockmeyer, "The polynomial-time hierarchy," Theor. Comput. Sci., vol. 3, no. 1, pp. 1-22, Oct. 1976.
27. T. Strzemecki, "Polynomial-time algorithms for the generation of prime implicants," J. Complex., vol. 8, no. 1, pp. 37-63, Mar. 1992.
28. M. Theobald and S. Nowick, "Fast heuristic and exact algorithms for two-level hazard-free logic minimization," IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst., vol. 17, no. 11, pp. 1130-1147, Nov. 1998.
29. P minimization problems," in Proc. 40th Annu. IEEE Symp. Foundations Computer Science (FOCS), New York, 1999, pp. 465-474.
30. _, "Approximability and completeness in the polynomial hierarchy," Ph.D. dissertation, Dept. Elect., Eng. Comput. Sci., Univ. California, Berkeley, 2000.
31. _, "The minimum equivalent DNF problem and shortest implicants," J. Comput. Syst. Sci., vol. 63, no. 4, pp. 597-611, Dec. 2001.
32. T. Villa, T. Kam, R. Brayton, and A. Sangiovanni-Vincentelli, Synthesis of FSMs: Logic Optimization. Norwell, MA: Kluwer, 1997.
33. V. Feldman, "Hardness of approximate two-level logic minimization and PAC learning with membership queries," ECCC, Potsdam-Babelsberg, Germany, Tech. Rep. TR05-127, 2005.
34. J. Goldsmith, M. Hagen, and M. Mundhenk, "Complexity of DNF and isomorphism of monotone formulas," in Proc. 30th Int. Symp. Mathematical Foundations Computer Science (MFCS), Gdansk, Poland, Aug. 2005, pp. 410-421.