Non-uniform Crossover in Genetic Algorithm Methods to Speed up the Generation of Test Patterns for Sequential Circuits

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Non-uniform Crossover in Genetic Algorithm
Methods to Speed up the Generation of Test
Patterns for Sequential Circuits
Michael Dimopoulos - Panagiotis Linardis
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Digital Circuits
inputs
outputs
Sequential Circuit
output f (inputs,time)
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Test Generation

• TESTING

• Apply a sequence of inputs to a circuit.
• Observe the output response and compare the
  response with a precomputed or expected
  response.
• Any discrepancy is said to constitute an error,
  the cause of which is a physical fault.

• STUCK-AT Fault Model

• In the faulty circuit, a single line/wire is
  S-a-0 or S-a-1.

• TEST GENERATION

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Test Problem Formulation

• Problem Formulation

FSM good M(I,O,S,d,?)
FSM faulty Mf(I,Of,Sf,df,?f)
For a given list of stuck-at faults
Ff1,f2,,fn Find a sequence of input
vectors V (Test Sequence) that detects the
faults in F.
?
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ATPG Methods

• Automatic Test Pattern Generation (ATPG)

• Optimum Test Set NP-Complete problem.

• ATPG Methods for Sequential Circuits

Stuck-at Fault Model

• Deterministic

• Simulation-based (random)

• Genetic Algorithms

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A Simple GA for ATPG
Initial
Crossover
(C)
(A)
(B)
Age Ngen
Mutation
fault simulation
(D)
(E)
Expand seq.
If (Ngen2) 0
Ngen Ngen1
(F)
Test
Ngen lt MAX_GENERATIONS
seq.
End
Test
seq.
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Encoding of the Individuals
Sequence of m vectors
n-input vector
n x m bit string
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Crossover Effect on Sequ Circuits
Detecting properties are preserved
1st vector
k-th vector
Detecting properties may be completely lost
LV vector
offsprings
parents
Vectors after the k-th, strongly depend on those
before the k-th
Crossover operation degrades to mutation
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Biased Crossover
1st vector
Detecting properties are preserved
Detecting properties may be completely lost
k-th vector
LV vector
offsprings
parents
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GA Test Generation Policy

• Slowly increase test sequ size
• Gradually expand candidate test sequences
• Append one new vector every three generations
• Direct crossover to tail of test sequ
• Try to optimize newly appended vectors
• Use non Uniform selection probability with
  emphasis on tail

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Proposed Distribution(NonUni)

• Square probability distribution (normalized) for
  crossover selection

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GATPG Algorithm
Create_random_population For each individual
Evaluate_fsimulation(individual)
Sort_population / with descending fit. value
/ ngen0 / generation num. / do
for (j0, i0 iltncross j 2, i) /
crossover /
cross_over(Individualj, Individualj1,
child1, child2) Evaluate_
fsimulation (child1) Evaluate_
fsimulation (child2) for
(i0 iltnmut i 2) / mutation /
mutation(Individual0, child1)
mutation(Individual1, child2)
Evaluate_ fsimulation (child1)
Evaluate_ fsimulation (child2)
Sort_population If ( (ngen 3) 0
) Expand_sequence(EXPAND_STEP)
Evaluate_fsim(Individual0) / check
best / ngen while
(ngenltMAX_GENERATIONS)
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Fitness Function
fitness if (ngen lt 0.25MAX_GENERATIONS) f1
else f2 where f1 20 . R1 R2 . R3
f2 20 . R1 R3 R2 . R4 . R5 and R1
fdetected R2 (sequ_length eff_length) /
sequ_length R3 factivated / (fremaining1)
R4 (faults propagated to FFs) / (num_FF .
factive . seq_length) R5 (faults propagated
to outputs) / (num_ouputs . factive . sequ_length)
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Experimental Results
ISCAS89 Benchmark Circuits

• POPULATION 32
• MAX_GENERATIONS 300
• PCROSSOVER 0.6
• PMUTATION 0.2
• EXPAND_STEP 1

GATPG parameters
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GATPG vs Uniform
Crossover Probability Distribution

• Uniform

• Sqr (GATPG)

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Experimental Results

• Comparison with other methods

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Experimental Results (cont)
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Experimental Results (cont)
GATPG HITEC Rudnick
Sequence Lengths
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Hybrid Methods
(b) circuit s400
(a) circuit s386
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Conclusion
GA for ATPG of Sequential Circuits

• Crossover operation degrades to mutation

• Non uniform (biased) probability distribution for
  cut-point selection in crossover operator

GATPG

• Slowly increase test sequ size

• Direct crossover to tail of test sequ