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CAS 721 Course Project

CAS 721 Course Project. Minimum Weighted Clique Cover of Test Set By Wei He (0041415). Contents. Background of problem Algorithm Implementation Combinatorial Computation Algorithm Constraints Summary. How to Test Chips?. Input Patterns. Output Patterns. … 11 … 00 … .. … .. … 01.

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CAS 721 Course Project

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  1. CAS 721Course Project Minimum Weighted Clique Cover of Test Set By Wei He (0041415)

  2. Contents • Background of problem • Algorithm Implementation • Combinatorial Computation • Algorithm Constraints • Summary

  3. How to Test Chips? Input Patterns Output Patterns …11 …00 ….. ….. …01 10… 00… ….. ….. 01… Very Large Scale Digital Circuit COMPARATOR STORED CORRECT RESPONSE Test Result Source: Essentials of Electronic Testing, Kluwer 2000

  4. Test Patterns Generation • Functional Test 1) Generate a complete set of test-patterns 2) Apply to small circuits • Structural Test 1) Discard equivalent stuck-at faults and the number of test patterns is decreased dramatically 2) Apply to VLSI testing mostly • ATPG Algorithm 1) Inject faulty Bits in test pattern 2) High fault coverage Source: Essentials of Electronic Testing, Kluwer 2000

  5. Problem Formulation • Given original Test Data : 64 bits long 1xxx1001x10xxx0xxx011x0x0xxx1xx0x00xx0x010xxx0x1xxx1xxx01xxx0xxx • How to remove the redundant bits? • Which way to achieve the most reduction? Divide to 8 test patterns with 8 bits long each pattern 0: 1 x x x 1 0 0 1 pattern 1: x 1 0 x x x 0 x pattern 2: x x 0 1 1 x 0 x pattern 3: 0 x x x 1 x x 0 pattern 4: x 0 0 x x 0 x 0 pattern 5: 1 0 x x x 0 x 1 pattern 6: x x x 1 x x x 0 pattern 7: 1 x x x 0 x x x

  6. Problem Refinement • Combine test patterns by using “don’t care” bits • Consider each pattern as a single node of a clique • Problem refined to achieve the lowest weight Complete Clique Cover

  7. Algorithm Implementation • match_count = 8 if two patterns i and k are exactly compatible • Edge[ i ] [ k ] = 1 if patterns i and k are exactly compatible otherwise Edge [ i ] [ k ] = 0 • To create a clique, check the Edge[ i ] [ k ] • Weight of edge measured by the compatibility of patterns weight [ i ] [ k ] = 8 such as 1 1 0 x 1 0 0 1 weight [ i ] [ k ] = 4 such as 1 0 x x 1 0 0 1

  8. Combinatorial Computing • Choose the clique with lowest weight • Solution to given test data P025: 1 0 0 1 1 0 0 1 P167: 1 1 0 1 0 0 0 0 P 34: 0 0 0 x 1 0 x 0 P025: 1 0 0 1 1 0 0 1 P467: 1 0 0 1 0 0 x 0 P 13: 0 0 0 x 1 0 x 0

  9. Combinatorial Computing • Clique 012 found with weight 16! • Clique 025 found with weight 12! • Clique 123 found with weight 20! • Clique 1236 found with weight 44! • Clique 126 found with weight 20! • Clique 136 found with weight 24! • Clique 167 found with weight 24! • Clique 234 found with weight 24! • Clique 2346 found with weight 48! • Clique 236 found with weight 24! • Clique 246 found with weight 24! • Clique 346 found with weight 24! • Clique 467 found with weight 24!

  10. Algorithm Constraints To apply this algorithm, require: • A feasible set of all the possible combinations beforehand • Feasible set always considered as a whole entity • Test data length not oversize • Dimension of test pattern matrix not fixed • Selected cliques to cover all the nodes

  11. Algorithm Refinement • Long Test Data should be partitioned based on the specification • Develop to search for the complete clique cover • Multiple solutions occur • Optimal solution not unique • Cliques increased tremendously • Long time computing • Get rid of redundant cliques

  12. Summary • Manufacturing defect inevitable, chips require test • Reduce the testing time by test data compression By this algorithm: • Test data matrix reduced from 8 x 8 to 3 x 8 • Optimal solution easily reached for short test data but usually not unique • Refinement required for long test data

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