On Properties of Kleene TDDs

Yukihiro IGUCHI  Tsutomu SASAO  Munehiro MATSUURA  

IEICE TRANSACTIONS on Information and Systems   Vol.E81-D   No.7   pp.716-723
Publication Date: 1998/07/25
Online ISSN: 
Print ISSN: 0916-8532
Type of Manuscript: Special Section PAPER (Special Issue on Test and Diagnosis of VLSI)
Category: Logic Simulation and Logic Optimization
binary decision diagram,  ternary decision diagram,  logic simulation,  ternary logic,  

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Three types of ternary decision diagrams (TDDs) are considered: AND -TDDs, EXOR-TDDs, and Kleene-TDDs. Kleene-TDDs are useful for logic simulation in the presence of unknown inputs. Let N(BDD:f), N(AND-TDD:f), and N(EXOR-TDD:f) be the number of non-terminal nodes in the BDD, the AND-TDD, and the EXOR-TDD for f, respectively. Let N(Kleene-TDD:) be the number of non-terminal nodes in the Kleene -TDD for , where is the regular ternary function corresponding to f. Then N(BDD:f) N(TDD:f). For parity functions, N(BDD:f)=N(AND-TDD:f)=N(EXOR-TDD:f)=N(Kleene-TDD:). For unate functions,N(BDD:f)=N(AND-TDD:f). The sizes of Kleene-TDDs are O(3n/n), and O(n3) for arbitrary functions, and symmetric functions, respectively. There exist a 2n-variable function, where Kleene-TDDs require O(n) nodes with the best order, while O(3n) nodes in the worst order.