Optimizing OBDDs Is Still Intractable for Monotone Functions

Optimizing the size of Ordered Binary Decision Diagrams is shown to be NP-complete for monotone Boolean functions. The same result for general Boolean functions was obtained by Bollig and Wegener recently.

[1]  Beate Bollig,et al.  Improving the Variable Ordering of OBDDs Is NP-Complete , 1996, IEEE Trans. Computers.

[2]  Uri Zwick A 4n Lower Bound on the Combinational Complexity of Certain Symmetric Boolean Functions over the Basis of Unate Dyadic Boolean Functions , 1991, SIAM J. Comput..

[3]  David S. Johnson,et al.  Stockmeyer: some simplified np-complete graph problems , 1976 .

[4]  Randal E. Bryant,et al.  Graph-Based Algorithms for Boolean Function Manipulation , 1986, IEEE Transactions on Computers.

[5]  David S. Johnson,et al.  Some Simplified NP-Complete Graph Problems , 1976, Theor. Comput. Sci..

[6]  Noga Alon,et al.  The monotone circuit complexity of boolean functions , 1987, Comb..

[7]  Shuzo Yajima,et al.  The Complexity of the Optimal Variable Ordering Problems of Shared Binary Decision Diagrams , 1993, ISAAC.

[8]  Éva Tardos,et al.  The gap between monotone and non-monotone circuit complexity is exponential , 1988, Comb..

[9]  Shuzo Yajima,et al.  Size of Ordered Binary Decision Diagrams Representing Threshold Functions , 1996, Theor. Comput. Sci..

[10]  Don E. Ross,et al.  Functional approaches to generating orderings for efficient symbolic representations , 1992, [1992] Proceedings 29th ACM/IEEE Design Automation Conference.

[11]  Claude E. Shannon,et al.  The synthesis of two-terminal switching circuits , 1949, Bell Syst. Tech. J..

[12]  Aaron D. Wyner,et al.  The Synthesis of TwoTerminal Switching Circuits , 1993 .

[13]  Saburo Muroga,et al.  Threshold logic and its applications , 1971 .