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U. Glaeser

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A corollary [50] of this theorem is that a synchronizing sequence leading to a defined state (all storage<br />

elements store 0 or 1) of all storage elements is upper bounded by 3n − 2n (n is the number of storage<br />

elements in the circuit) assuming that there is no global reset possibility. The reason is that a 3-valued<br />

logic is used starting from the undefined state. With n storage elements, the number of states in the<br />

circuit is upper bounded to 3n. Because no state repetition is allowed and the number of states where<br />

all storage elements have a defined state, is 2n, the storage elements have a defined state after applying<br />

an input sequence with length at most 3n − 2n. A second result is that all reachable states of the circuit<br />

can be reached by a sequence, which has a maximum length of 3n.<br />

Usually, the test generation results into a set of states after each considered time frame with 2y elements,<br />

y is the number of x-values in the storage elements. For this reason, we use “set of states” instead of<br />

“state” as notation here.<br />

To avoid long test sequences with state repetitions, SEMILET checks the propagation and the justification<br />

phases whether the actual set of states is a subset of a set of states, which occurred a number of time frames<br />

earlier in the test generation. For this purpose, the good and the faulty machines are considered during<br />

propagation while only the good machine is considered during justification. If the actual set of states is a<br />

subset of an earlier set of states, a backtrack to the previous time frame is performed and test generation<br />

is continued without loosing the completeness of the algorithm.<br />

Use of Global Set and Reset Signals in ATPG<br />

If the circuits consist of global set and reset signals, test generation can take advantage of this. A global<br />

set signal effects that every flip-flop in the circuit is set to 1, and a global reset signal effects that every<br />

flip-flop is set to value 0. In the justification phase of the algorithm it is possible to make use of global<br />

set and reset signals:<br />

• A set can be performed, if in the current state in ATPG there is no 0-requirement.<br />

• A reset can be performed, if in the current state in ATPG there is no 1-requirement.<br />

SEMILET can optionally use these features. The results with ISCAS-benchmark circuits in the subsection<br />

on “Experimental Results.” Table 45.8 shows that use of global set- and/or reset-signals results in increased<br />

fault coverage and/or decreased CPU time as expected.<br />

Experimental Results<br />

The authors have developed SEMILET for test generation for synchronous sequential circuits. SEMILET<br />

makes use of the FOGBUSTER-algorithm and has mixed level capabilities like MILEF. In the actual state<br />

of implementation, SEMILET can handle 3 fault models:<br />

• Stuck-at with overcurrent detection (mode 1)<br />

• Stuck-at with state propagation (mode 2)<br />

SEMILET is programmed in C++ with about 30,000 lines of code. It is prepared for sequential test<br />

generation with two levels of hierarchy, the switch-level and the gate-level (see also [9]).<br />

The overcurrent techniques are reported in [23,24]. Generation of test patterns for overcurrent techniques<br />

is in general easier in comparison with the test generation, which needs propagation techniques.<br />

The authors found that, if a stuck-at test is required, in many cases it makes sense to generate IDDQ<br />

patterns and simulate them like “intelligent random patterns” in a first phase of test generation. For all<br />

the faults that are not detected by these patterns, a “normal” stuck-at test pattern set is computed. Thus<br />

the test generation mode 3 is done in two phases. Table 45.9 shows experimental results of SEMILET<br />

with fault model mode 1 in comparison with results of GENTEST [44] for some ISCAS ’89 benchmark<br />

[46] circuits. The times of GENEST, HITEC, and SEMILET were measured on a SUN 4/260. The efficiency<br />

is computed as follows:<br />

© 2002 by CRC Press LLC<br />

efficiency =<br />

(redundant faults + detected faults)/total number of faults

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