• Publication
  • 1988
  • Issue No. 7 - July
  • Abstract - Meaningful Special Classes of Ternary Logic Functions-Regular Ternary Logic Functions and Ternary Majority Functions
 This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Meaningful Special Classes of Ternary Logic Functions-Regular Ternary Logic Functions and Ternary Majority Functions
July 1988 (vol. 37 no. 7)
pp. 799-806
Special ternary logic functions, namely, regular functions suitable for treating ambiguity and majority functions based on an extended majority principle are considered. The one-to-one correspondence between n-ary monotone regular ternary logic functions and (n+1)-ary monotone Boolean functions is investigated, as well as the one-to-one correspondence between n-ary monotone ternary majority fun

[1] M. Mukaidono, "Regular ternary logic functions-Ternary logic functions suitable for treating ambiguity," inProc. IEEE 13th Int. Symp. Multiple-Valued Logic, May 1983, pp. 286-291.
[2] M. Mukaidono, "Regular ternary logic functions--Ternary logic functions suitable for treating ambiguity,"IEEE Trans. Comput., vol. C-35, pp. 179-183, Feb. 1986; available also inProc. IEEE 13th Int. Symp. Multiple-Valued Logic, May 1983, pp. 286-291.
[3] M. Mukaidono, "On theB-ternary logical functions-A ternary logic considering ambiguity,"Syst. Comput. Contr., vol. 3, pp. 27-36, Mar. 1972.
[4] M. Mukaidono, "The B-ternary logic and its application to the detection of hazards in combinational switching circuits," inProc. IEEE 8th Int. Symp. Multiple-Valued Logic, May 1978, pp. 269-275.
[5] H. Tatsumi and M. Mukaidono, "Enumerating regular ternary logic functions,"Trans. IECE Japan, vol. J68-D, pp. 1027-1034, May 1985.
[6] Y. Yamamoto and S. Fujita, "Three-valued majority functions,"Trans. IECE Japan, vol. J63-D, pp. 493-500, June 1980.
[7] H. Mine and Y. Yamamoto, "Testing and realization of three-valued majority functions," inProc. IEEE 11th Int. Symp. Multiple-Valued Logic, May 1981, pp. 157-162.
[8] S. L. Hurst, "Multiple-valued logic-Its status and its future,"IEEE Trans. Comput., vol. C-33, pp. 1160-1179, Dec. 1984.
[9] Y. Yamamoto and S. Fujita, "Multiple-valued majority functions with the same logical expressions as binary threshold functions,"Trans. IECE Japan, vol. J64-D, pp. 172-173, Feb. 1981.
[10] Y. Yamamoto and S. Fujita, "Error correctable many-valued majority elements,"Trans. IECE Japan, vol. E-67, pp. 47-48, Jan. 1984.
[11] T. Kitahashi, "Social decision and ternary majority functions," inProc. IEEE 12th Int. Symp. Multiple-Valued Logic, May 1982, pp. 159-162.
[12] H. Mine, Y. Yamamoto, and S. Fujita, "A method of determining the functional form of three-valued majority functions,"Trans. IECE Japan, vol. E-64, pp. 604-605, Sept. 1981.
[13] Y. Hata, Y. Miyoshi, K. Nakashima, and K. Yamato, "A necessary and sufficient condition for three-valued majority functions," inProc. IEEE 15th Int. Symp. Multiple-Valued Logic, May 1985, pp. 286- 291.
[14] H. Mine, Y. Yamamoto, and S. Fujita, "Generation of ternary majority functions of four or less variables," inProc. IEEE 13th Int. Symp. Multiple-Valued Logic, May 1983, pp. 84-91.
[15] H. Tatsumi and M. Mukaidono, "Unate regular ternary logic functions and three-valued majority functions,"Note Multiple-Valued Logic Japan, vol. 3, 1985.
[16] S. C. Kleene,Introduction to Metamathematics. Amsterdam: North-Holland, 1952, pp. 332-340.
[17] M. Goto, "Application of logical mathematics to the theory of relay networks,"J. IEE Japan, vol. 69, 1949.
[18] M. Mukaidono and I. G. Rosenberg, "K-valued functions for treating ambiguities: Their clone and a normal form," inProc. IEEE 16th Int. Symp. Multiple-Valued Logic, May 1986, pp. 204-211.
[19] M. Mukaidono, "Some kinds of functional completeness of ternary logic functions," inProc. IEEE 10th Int. Symp. Multiple-Valued logic, May 1980, pp. 81-87.
[20] M. Mukaidono, "On the mathematical structure of C-type fail-safe logic,"Electron. Commun. Japan, IEEE, vol. 52-C, pp. 188-195, Dec. 1969.
[21] M. Yoeli and S. Rinon, "Application of ternary algabra to the static hazard,"J. ACM, vol. 11, pp. 84-97, Jan. 1964.
[22] S. Muroga, I. Toda, and S. Takasu, "Theory of majority decision elements,"J. Franklin Instit., vol. 271, pp. 376-418, May 1961.
[23] R. O. Winder, "Enumeration of seven argument threshold functions,"IEEE Trans. Electron. Comput., vol. EC-14, pp. 315-325, 1965.
[24] S. Muroga, T. Tsuboi, and C. r. Baugh, "Enumeration of threshold functions of eight variables,"IEEE Trans. Comput., vol. C-19, pp. 818-825, Sept. 1970.
[25] C. Moraga, "A monograph on ternary threshold logic,"Computer Science and Multiple-Valued Logic. Amsterdam: North-Holland, 1984, pp. 329-368.
[26] M. Mukaidono, "Regular ternary logic functions and their application to fail-safe logic," inProc. IEEE Workshop Languages Automat., 1986, pp. 232-236.
[27] Y. Yamamoto and S. Fujita, "Relationship betweenP-valued majority functions andP-valued threshold functions,"IEEE Trans. Comput., to be published.

Index Terms:
ternary logic functions; regular ternary logic functions; ternary majority functions; Boolean functions; Boolean functions; many-valued logics.
Citation:
Y. Yamamoto, M. Mukaidono, "Meaningful Special Classes of Ternary Logic Functions-Regular Ternary Logic Functions and Ternary Majority Functions," IEEE Transactions on Computers, vol. 37, no. 7, pp. 799-806, July 1988, doi:10.1109/12.2225
Usage of this product signifies your acceptance of the Terms of Use.