7/25/2019 4.Test Generation Comb 4

1/22

1

ehrdad Nourani

Dept. of EEUniv. of Texas at Dallas

EEDG/CE 6303: Testing and Testable Design

7/25/2019 4.Test Generation Comb 4

2/22

2

Test Generation for

ombinational ircuits

Session 04

7/25/2019 4.Test Generation Comb 4

3/22

3

Accelerating Test Generation

There are many approaches in the literature trying to speed

up the test generation process. Two main categories

Deterministic: Guaranteed to reduce search complexity

Heuristic: Likely to reduce search complexity

Even a deterministic technique may not reduce overallcomplexity if the complexity required to implement thetechnique exceedsthe reduction in search complexity

7/25/2019 4.Test Generation Comb 4

4/22

4

Testability Measures

7/25/2019 4.Test Generation Comb 4

5/22

5

Purpose

Need approximate measure of:

Difficulty of setting internal circuit lines to 0 or 1 by settingprimary circuit inputs

Difficulty of observing internal circuit lines by observing primaryoutputs

Uses:Analysis of difficulty of testing internal circuit partsredesign or

add special test hardware

Guidance for algorithms computing test patternsavoid usinghard-to-control lines

Estimation of fault coverage Estimation of test vector length

7/25/2019 4.Test Generation Comb 4

6/22

6

Control theory

Rutman 1972 -- First definition of controllability Goldstein 1979 -- SCOAP

First definition of observability

First elegant formulation

First efficient algorithm to compute controllability and

observability Parker & McCluskey 1975

Definition of Probabilistic Controllability

Brglez 1984 -- COP

1stprobabilistic measures

Seth, Pan & Agrawal 1985PREDICT

1stexact probabilistic measures

Origin

7/25/2019 4.Test Generation Comb 4

7/22

7

Involves Circuit Topological analysis, but no testvectors and no search algorithmStatic analysis

Linear computational complexity

otherwise, is pointlessmight as well use automatictest-pattern generation and calculate: Exact fault coverage

Exact test vectors

Testability Analysis

7/25/2019 4.Test Generation Comb 4

8/22

8

SCOAPSandia Controllability and ObservabilityAnalysis Program

Combinational measures:CC0Difficulty of setting circuit line to logic 0

CC1Difficulty of setting circuit line to logic 1CODifficulty of observing a circuit line

Sequential measuresanalogous:SC0

SC1SO

SCOAP and Its Metrics

7/25/2019 4.Test Generation Comb 4

9/22

9

These metrics reflect the level of difficulty

Controllabilities1 (easiest) to infinity (hardest)

Observabilities0 (easiest) to infinity (hardest)

Combinational measures:

Roughly proportional to # circuit lines that must beset to control or observe given line

Sequential measures:Roughly proportional to # times a flip-flop must be

clocked to control or observe given line

SCOAP and Its Metrics

7/25/2019 4.Test Generation Comb 4

10/22

10

AND gate O/P 0 controllability:

output_controllability = min (input_controllabilities) + 1

AND gate O/P 1 controllability:

output_controllability = S (input_controllabilities)+ 1

XOR gate O/P controllabilityoutput_controllability = min (controllabilities of each input set) + 1

To observe a gate input, observe output and makeother input values non-controlling

To observe a fanout stem, observe it throughbranch with best observability

Fanout Stem observability:or min (some or all fanout branch observabilities)

Metrics Computation

7/25/2019 4.Test Generation Comb 4

11/22

11

Controllability Examples

CC0(a)CC1(a)

CC0(zi)=CC0(a)CC1(zi)=CC1(a)

7/25/2019 4.Test Generation Comb 4

12/22

12

Observability Examples

7/25/2019 4.Test Generation Comb 4

13/22

13

Exact computation of measures is NP-complete

and impractical. SCOAP measures wrongly assume that controlling

or observing x, y, z are independent eventsCC0 (x), CC0 (y), CC0 (z)correlate

CC1 (x), CC1 (y), CC1 (z)correlate

CO (x), CO (y), CO (z)correlate

x

y

z

Errors Due to Reconverging Fanouts

7/25/2019 4.Test Generation Comb 4

14/22

14

Controllability Example - Level 0

Circled numbers give level number.

Notation is: (CC0, CC1)

7/25/2019 4.Test Generation Comb 4

15/22

15

Controllability Example - Level 1 and 2

7/25/2019 4.Test Generation Comb 4

16/22

16

Controllability Example - Level 3 and 4

7/25/2019 4.Test Generation Comb 4

17/22

17

Observability Example Level 1

Squared numbers give level number.

Notation is: (CC0, CC1) CO

7/25/2019 4.Test Generation Comb 4

18/22

18

Observability Example Level 2

7/25/2019 4.Test Generation Comb 4

19/22

19

Observability Example Level 3 & 4

7/25/2019 4.Test Generation Comb 4

20/22

20

Sequential Measure Differences

Combinational

Increment CC0, CC1, COwhenever you pass through agate, either forwards or backwards

Sequential

Increment SC0, SC1, SOonly when you pass through aflip-flop, either forwards or backwards, to Q, Q, D, C,SET, or RESET

Both

Must iterate on feedback loops until controllabilitiesstabilize

7/25/2019 4.Test Generation Comb 4

21/22

21

1. For all PIs, CC0= CC1= 1 [SC0= SC1= 0]

2. For all other nodes, CC0= CC1= [SC0= SC1= ]

3. Go from PIs to POS, using CC [SC] equations to getcontrollabilities [-- Iterate on loops until SCstabilizes --

convergence guaranteed]4. For all POs, set CO=0 [SO= 0]

5. For all other nodes, CO= [SO= ]

6. Work from POs to PIs, Use CO[SO] and controllabilities to

get observabilities. Fanout stem CO= min branch (COi),[SO= min branch (SOi)]

7. If a CCor CO[SCor SO] is , that node is uncontrollable(or unobservable)

Testability Computation Algorithm

7/25/2019 4.Test Generation Comb 4

22/22

22

Test Vector Length Prediction

To detect a fault at x, we need to

Set x to the opposite value from the fault Observe x at PO

Compute testabilitiesfor stuck-at faults

T(x sa0) = CC1(x) + CO(x)

T(x sa1) = CC0(x) + CO(x)

Testabilityindex= log ST (fi) , i.e. computed for all faults fi

LinearRelationship