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An Iterative Heuristic for State Justification in Sequential Automatic Test Pattern Generation

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Title: An Iterative Heuristic for State Justification in Sequential Automatic Test Pattern Generation


1
An Iterative Heuristic for State Justification
in Sequential Automatic Test Pattern Generation
  • Aiman H. El-Maleh Sadiq M. Sait Syed Z. Shazli
  • Department of Computer Engineering
  • King Fahd University of Petroleum and Minerals
  • Dhahran, Saudi Arabia

2
Outline
  • Motivation
  • Sequential Test Generation
  • Genetic Algorithms for Test Generation
  • Problem definition existing solutions
  • Proposed approach
  • Experimental results
  • Comparison with other approaches
  • Conclusions

3
Motivation
  • Testing of ICs accounts for significant
    percentage of design production costs.
  • Deterministic, fault-oriented sequential circuit
    test generation is highly complex and time
    consuming.
  • Hard to detect faults require very high CPU time
    and often not detected.
  • New approaches needed to reduce execution time
    and improve fault coverage.
  • Evolutionary algorithms effective in solving many
    search and optimization problems.
  • Genetic algorithms

4
Sequential Test Generation
  • A sequential circuit has memory in addition to
    combinational logic.
  • Testing for a fault in a sequential circuit
    requires
  • A vector to activate the fault
  • A propagation sequence to propagate the fault
    effect to a primary output
  • A state justification sequence to justify the
    required state on the memory elements
  • State justification using deterministic
    algorithms is a difficult problem with high
    execution times.

5
Genetic Algorithms for Test Generation
  • Genetic algorithms
  • Basic idea is population improves with each
    generation
  • Population A set of input vectors or vector
    sequences.
  • Fitness function Based on fault or logic
    simulation of candidate vectors or sequences
  • Regeneration rules (heuristics) Members with
    higher fitness function values are selected to
    produce new members via transformations like
    mutation and crossover.

6
Problem Definition Existing Solutions
  • State justification Process of finding a
    sequence of inputs that will drive the state
    machine from the reset (or unknown or KNOWN?)
    state to the present state required by the test.
  • Existing solutions
  • Deterministic Algorithms
  • State justification involves backtracking, high
    CPU time
  • Hard to detect faults often not detected
  • More effective for control-dominant circuits
  • Poor performance for circuits with large number
    of invalid states (retimed circuits)
  • Able to identify redundant faults

7
Existing Solutions
  • Simulation-based Approaches
  • Processing occurs in forward direction only
  • More effective for data-path-dominant circuits
  • Unable to identify redundant faults
  • A Hybrid approach is needed
  • Deterministic algorithms for fault activation and
    propagation
  • State justification using Simulation-based
    approaches

8
Proposed Hybrid State Justification Framework
Select Target Fault
Run Deterministic ATPG
Y
Fault detected
Fault simulate generated sequence
N
Justify state using Genetic Algorithm
9
The GA-Based State Justification Approach in
Hsiao 98
  • A chromosome is a sequence of test vectors (fixed
    length)
  • Objective To genetically engineer a state
    justification sequence
  • Logic simulation is used to get the state reached
    by the sequence
  • The fitness function matches only the last state
    reached, with the desired state.
  • Drawbacks of the approach
  • Length of the sequence depends on structural
    sequential depth of the circuit
  • Quality of intermediate states reached is not
    considered while justifying a target state

10
The Approach used in Hsiao 98
Desired state 10x10x
Fit (P1) 3 / 4
Fit (P2) 3 / 4
Fit (Child) 1
11
Proposed GA-Based State Justification
  • We apply GA while moving from a state to a state
  • A chromosome consists of a single vector instead
    of a sequence of vectors
  • State justification sequences are genetically
    engineered vector-by-vector
  • Fitness based on number of matching bits between
    reached and desired state (Hamming distance)
  • A Tabu List containing the last visited states is
    maintained.
  • Prevents algorithm from visiting recently visited
    FSM states
  • If FSM state reached is Tabu, next fit vector is
    chosen

12
The Proposed Approach
Reset state 0000
Target state 11x0
C1 010011
0001 Fit(P1) 0 / 3
C2 110101
0010 Fit(P2) 1 / 3
C3 010101
0110 Fit(C) 2 / 3
010101 is added to the state justification
sequence
0110 becomes the new reset state
13
Proposed GA-Based State Justification
  • Backtrack limit
  • Backtrack to last visited state when all
    chromosomes produce states that are Tabu (happens
    in control dominated ckts)
  • Algorithm stops searching for a state when limit
    exceeded
  • Nlimit
  • A minimum limit on the number of states to be
    traversed for reaching an objective state
  • Algorithm stops if fitness of current state is
    less than average fitness of last Nlimit visited
    states
  • If desired state is reached
  • Compare all reached states by the derived
    sequence to desired states
  • All desired states reached are removed

14
Proposed GA-Based State Justification
15
Experimental results
  • Benchmark circuits
  • ISCAS 89 sequential circuits
  • Retimed circuits (Used high CPU time in
    deterministic ATPG of HITEC)
  • List of desired states
  • Ran HITEC ATPG for 109 backtracks to remove
    undetectable faults
  • States generated for all aborted faults (not
    detected)
  • States relaxed to keep only necessary
    requirements
  • States merged to reduce number of desired states

16
GA Parameters used
  • The initial population is randomly generated
  • Rate of crossover is 1
  • Mutation rate is 0.01
  • Single point crossover
  • Roulette-wheel used for selecting parents
  • Three replacement strategies explored
  • (n1) replacement strategy
  • Worst member of previous generation replaced new
    chromosome if new chromosome fitter
  • Average fitness monotonically increases in every
    generation
  • Random-Elitist strategy
  • N/2 crossovers in every generation N is
    population size
  • Fittest half of chromosomes transferred directly
    to next generation
  • Other half selected randomly
  • Roulette Elitist strategy
  • Other half selected by roulette wheel

17
Effect of Replacement Policies
18
Average Best Fitness
  • (n1) replacement strategy
  • Lowest execution time
  • Reached comparable number of states
  • (Best in most circuits except two)

19
Quality of States Reached
Reached State
Unreached State
20
Recommended Parameters
  • Our technique
  • Population size 32
  • Generations 400
  • TLS 15
  • Nlimit 1.5 (DFF)
  • BT Limit 10
  • Technique in Hsiao 98
  • Length of sequence 4seq.depth
  • A population size of 32
  • Number of generations is 8
  • Two-point uniform crossover probability of
    crossover is 1.
  • Any vector in the chromosome is replaced with
    another random vector in mutation probability of
    mutation is 0.01
  • Tournament selection mechanism

21
Recommended vs. Best
22
Comparison with Hsiao 98
23
Comparison with Hsiao 98
24
Comparison with Hsiao 98
25
Conclusions
  • A hybrid ATPG approach for sequential circuits
    involving deterministic and GA-based state
    justification
  • A novel state justification procedure based on GA
  • Genetic engineering of a sequence vector by
    vector.
  • Advantage of dynamically determining the length
    of justification sequence
  • Benefit of taking quality of intermediate states
    into account
  • Use of Tabu List to prevent the algorithm from
    visiting previously visited state
  • Comparison of three replacement strategies
  • (n1) replacement strategy gave better results
  • Achieved better results than the technique in
    Hsiao 98
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