This Article 
   
 Share 
   
 Bibliographic References 
   
 Add to: 
 
Digg
Furl
Spurl
Blink
Simpy
Google
Del.icio.us
Y!MyWeb
 
 Search 
   
Computational Complexity of Controllability/Observability Problems for Combinational Circuits
June 1990 (vol. 39 no. 6)
pp. 762-767

The computational complexity of fault detection problems and various controllability and observability problems for combinational logic circuits are analyzed. It is shown that the fault detection problem is still NP-complete for monotone circuits limited in fanout, i.e. when the number of signal lines which can out from a signal line is limited to two. It is also shown that the observability problem for unate circuits is NP-complete, but that the controllability problem for unate circuits can be solved in time complexity O(m), where m is the number of lines in a circuit. Two classes of circuits, called k-binate-bounded circuits and k-bounded circuits, are then introduced. For k-binate-bounded circuits the controllability problem is solvable in polynomial time, and for k-bounded circuits the fault detection problem is solvable in polynomial time, when k>or=log p(m) for some polynomial p(m). The class of k-bounded circuits includes many practical circuits such as decoders, adders, one-dimensional cellular arrays, and two-dimensional cellular arrays.

[1] H. Fujiwara,Logic Testing and Design for Testability. Cambridge, MA: MIT Press, 1985.
[2] P. H. Ibarra and S. K. Sahni, "Polynomially complete fault detection problems,"IEEE Trans. Comput., vol. C-24, pp. 242-249, Mar. 1975.
[3] H. Fujiwara and S. Toida, "The complexity of fault detection problems for combinational logic circuits,"IEEE Trans. Comput., vol. C-31, pp. 555-560, June 1982.
[4] M. R. Garey and D. S. Johnson,Computers and Intractability: A Guide to Theory of NP-Completeness. San Francisco, CA: Freeman, 1979.
[5] S. A. Cook, "The complexity of theorem-proving procedures," inProc. 3rd Annu. ACM Symp. Theory of Comput., 1971, pp. 151-158.
[6] H. Fujiwara and S. Toida, "The complexity of fault detection problems for combinational logic circuits," Dep. Syst. Design, Univ. of Waterloo, Waterloo, Ont., Canada, Tech. Rep. 78-P-HW-150681, June 1981.

Index Terms:
controllability; observability; combinational circuits; computational complexity; fault detection; NP-complete; monotone circuits; k-binate-bounded circuits; k-bounded circuits; polynomial time; combinatorial circuits; computational complexity; controllability; fault location; observability.
Citation:
H. Fujiwara, "Computational Complexity of Controllability/Observability Problems for Combinational Circuits," IEEE Transactions on Computers, vol. 39, no. 6, pp. 762-767, June 1990, doi:10.1109/12.53597
Usage of this product signifies your acceptance of the Terms of Use.