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Y. Hata, K. Nakashima, K. Yamato, "Some Fundamental Properties of MultipleValued Kleenean Functions and Determination of Their Logic Formulas," IEEE Transactions on Computers, vol. 42, no. 8, pp. 950961, August, 1993.  
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@article{ 10.1109/12.238485, author = {Y. Hata and K. Nakashima and K. Yamato}, title = {Some Fundamental Properties of MultipleValued Kleenean Functions and Determination of Their Logic Formulas}, journal ={IEEE Transactions on Computers}, volume = {42}, number = {8}, issn = {00189340}, year = {1993}, pages = {950961}, doi = {http://doi.ieeecomputersociety.org/10.1109/12.238485}, publisher = {IEEE Computer Society}, address = {Los Alamitos, CA, USA}, }  
RefWorks Procite/RefMan/Endnote  x  
TY  JOUR JO  IEEE Transactions on Computers TI  Some Fundamental Properties of MultipleValued Kleenean Functions and Determination of Their Logic Formulas IS  8 SN  00189340 SP950 EP961 EPD  950961 A1  Y. Hata, A1  K. Nakashima, A1  K. Yamato, PY  1993 KW  multiplevalued Kleenean functions; logic formulas; Kleene algebra; logic functions; variables; constants; fuzzy logic functions; regular ternary logic functions; Bternary logic functions; monotonic ternary input functions; pvalued unate function; mapping relations; fuzzy logic; manyvalued logics. VL  42 JA  IEEE Transactions on Computers ER   
Multiplevalued Kleenean functions that are models of a Kleene algebra and are logic functions expressed by logic formulas composed of variables, constants, and logic operations AND OR, and NOT are discussed. The set of Kleenean functions, is a model with the largest number of logic functions among existing models of a Kleene algebra, such as fuzzy logic functions, regular ternary logic functions, and Bternary logic functions. Mainly, it is shown that any pvalued Kleenean function is derived from a monotonic ternary input functions and any pvalued unate function is derived from a unate binary input function. The mapping relations between them and the method to determine the logic formula of the Kleenean function and unate function from that of the monotonic ternary input function and unate binary input function, respectively, are classified. 7orlessvalued Kleenean functions and unate functions of 3orfewer variables are enumerated. It is known that the number of pvalued Kleenean functions increases stepwise and that of unate functions increases smoothly as p becomes larger.
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