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<p>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.</p>
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.
H. Fujiwara, "Computational Complexity of Controllability/Observability Problems for Combinational Circuits", IEEE Transactions on Computers, vol. 39, no. , pp. 762-767, June 1990, doi:10.1109/12.53597
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