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# Lecture_9 - Overview Major ATPG algorithms Definitions...

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9/30/2011 1 ECE 553: TESTING AND TESTABLE DESIGN OF DIGITAL SYSTES Combinational ATPG 9/30/2011 2 Overview Major ATPG algorithms Definitions D-Algorithm (Roth) -- 1966 D-cubes Bridging faults Logic gate function change faults PODEM (Goel) -- 1981 X-Path-Check Backtracing Summary 9/30/2011 3 Forward Implication Results in logic gate inputs that are significantly labeled so that output is uniquely determined AND gate forward implication table: 9/30/2011 4 Backward Implication Unique determination of all gate inputs when the gate output and some of the inputs are given 9/30/2011 5 Implication Stack, Decision Tree, and Backtrack 0 1 0 0 0 0 0 1 1 1 1 E F B 1 Unexplored Present Assignment Searched and Infeasible 9/30/2011 6 Objectives and Backtracing in ATPG Objective – desired signal value goal for ATPG Guides it away from infeasible/hard solutions Uses heuristics Backtrace – Determines which primary input and value to set to achieve objective Use heuristics such as nearest PI Forward trace Determines gate through which the fault effect should be sensitized Use heuristics such as output that is closest to the present fault effect

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9/30/2011 2 9/30/2011 7 Branch-and-Bound Search Efficiently searches binary search tree Branching – At each tree level, selects which input variable to set to what value Bounding – Avoids exploring large tree portions by artificially restricting search decision choices Complete exploration is impractical Uses heuristics Backtracking – Search fails, therefore undo some of the work completed and start searching from a location where search options still exist 9/30/2011 8 D-Algorithm – Roth (1966) Fundamental concepts invented: First complete ATPG algorithm D-Cube D-Calculus Implications – forward and backward Implication stack Backtrack Test Search Space 9/30/2011 9 Singular Cover Example Minimal set of logic signal assignments to represent a function show prime implicants and prime implicates of Karnaugh map (with explicitly showing the outputs too) Gate AND 1 2 3 Inputs A 0 X 1 B X 0 1 Output d 0 0 1 Gate NOR 1 2 3 Inputs 1 X 0 e X 1 0 Output F 0 0 1 9/30/2011 10 Primitive D-Cube of Failure Models circuit faults: Stuck-at-0 Stuck-at-1 Other faults, such as Bridging fault (short circuit) Arbitrary change in logic function AND Output sa0: 1 1 D AND Output sa1: 0 X D X 0 D Wire sa0: D Propagation D-cube – models conditions under which fault effect propagates through gate 9/30/2011 11 Construction of Primitive D-Cubes of Failure 1. Make cube set a 1 when good machine output is 1 and set a 0 when good machine output is 0 2. Make cube set b 1 when failing machine output is 1 and b 0 when it is 0 3. Change a 1 outputs to 0 and D-intersect each cube with every b 0 . If intersection works, change output of cube to D 4. Change a 0 outputs to 1 and D-intersect each cube with every b 1 . If intersection works,
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Lecture_9 - Overview Major ATPG algorithms Definitions...

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