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Checking Sequence Generation Using State Distinguishing Subsequences

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### Checking Sequence Generation Using State Distinguishing Subsequences

Adenilso Simão*, Alexandre Petrenko

Centre de recherche informatique de Montreal (CRIM)

*On a leave from the Universidade de São Paulo

A-MOST’09 @ Denver, April 1st, 2009

Outline

- Problem statement
- Previous work
- Contribution of this work
- Example
- Conclusion

Problem Statement

- Given a specification FSM with n states
- Deterministic, Minimal, Complete
- Given a black box implementation FSM in the fault domain
- All FSMs with at most n states
- Generate a checking sequence
- To detect all non-equivalent implementations

Key Issue

- How to recognize states in the implementation
- State distinguishing subsequences
- Same input, but with different outputs
- Different distinguishing capacities

SK02

YY06

C+05

1960

1970

1980

1990

2000

2010

B74

H65

G70

KK68

SP08

U+97

HU06

HU02

A+91

SP09

Previous Work- Hennie, 1965
- Seminal paper
- Problem setting
- Efficient method
- Ad hoc
- Distinguishing sequence

SK02

YY06

C+05

1960

1970

1980

1990

2000

2010

B74

H65

G70

KK68

SP08

U+97

HU06

HU02

A+91

SP09

Previous Work- Kohavi and Kohavi, 1968
- Improves (Hennie, 1965)
- Variable length distinguishing sequence
- Prefix of a sistinguishing sequence

SK02

YY06

C+05

1960

1970

1980

1990

2000

2010

B74

H65

G70

KK68

SP08

U+97

HU06

HU02

A+91

SP09

Previous Work- Gonenc, 1970
- A method for checking sequence generation
- Graph based
- Distinguishing sequences
- Formalizes (Hennie, 1965)

SK02

YY06

C+05

1960

1970

1980

1990

2000

2010

B74

H65

G70

KK68

SP08

U+97

HU06

HU02

A+91

SP09

Previous Work- Boute, 1974
- Distinguishing sets
- Also known as adaptive distinguishing sequence
- Generalizes (Hennie, 1965)

SK02

YY06

C+05

1960

1970

1980

1990

2000

2010

B74

H65

G70

KK68

SP08

U+97

HU06

HU02

A+91

SP09

Previous Work- Aho et al., 1991
- Uses Unique Input/Output Sequences (UIOs)
- Incomplete fault coverage
- Optimization approach
- Rural Chinese Postman Problem

SK02

YY06

C+05

1960

1970

1980

1990

2000

2010

B74

H65

G70

KK68

SP08

U+97

HU06

HU02

A+91

SP09

Previous Work- Ural et al., 1997
- Builds on (Aho et al. 1991)
- Improves (Gonenc, 1970)
- State Recognition and Transition Verification
- Uses distinguishing sequences

SK02

YY06

C+05

1960

1970

1980

1990

2000

2010

B74

H65

G70

KK68

SP08

U+97

HU06

HU02

A+91

SP09

Previous Work- Hierons and Ural, 2002
- Improves (Ural et al. 1997)
- Uses distinguishing sequences

SK02

YY06

C+05

1960

1970

1980

1990

2000

2010

B74

H65

G70

KK68

SP08

U+97

HU06

HU02

A+91

SP09

Previous Work- Serdar and Kuo-Chung, 2002
- Improves (Gonenc, 1970)
- Uses distinguishing sequences and UIOs

SK02

YY06

C+05

1960

1970

1980

1990

2000

2010

B74

H65

G70

KK68

SP08

U+97

HU06

HU02

A+91

SP09

Previous Work- Chen el al. 2005
- Improves (Ural et al., 1997)
- Avoids redundant transition verification

SK02

YY06

C+05

1960

1970

1980

1990

2000

2010

B74

H65

G70

KK68

SP08

U+97

HU06

HU02

A+91

SP09

Previous Work- Yalcin and Yenigun, 2006
- Improves (Ural et al., 1997)
- Uses distinguishing sequences and UIOs
- Hierons and Ural, 2006
- Improves (Hierons and Ural, 2002)
- Uses distinguishing sequences

SK02

YY06

C+05

1960

1970

1980

1990

2000

2010

B74

H65

G70

KK68

SP08

U+97

HU06

HU02

A+91

SP09

Previous Work- Simao and Petrenko, 2008 (SP08)
- Different approach for state recognition
- Confirmed sets (of sequences)
- Local optimization
- Experimental results
- Uses distinguishing sets

Contribution of this work

- New possibilities for shortening checking sequences
- Output-confirmed sequence
- Convergence/divergence
- Sequence confirmation and transition verification using confirmed sets
- Even if distinguishing sequence or UIO is not applied in a given state

Contribution of this work

- Generation Method
- Uses various distinguishing sequences
- Distinguishing sets
- UIOs
- State identifier in a subset of states
- Local optimization of transfer sequences
- No global optimization
- Overlapping

Example

- Hierons and Ural, 2006
- Checking sequence of length 64
- Chen et al., 2005
- Checking sequence of length 44
- Simao and Petrenko, 2008
- Checking sequence of length 43
- Proposed method
- Checking sequence of length 36

Other Examples

- Serdar and Kuo-chung, 2002
- Checking sequence of length 80
- Our method: 36
- Yalcin and Yenigun, 2006
- Checking sequence of length 26
- Our method: 13

Future work

- To integrate the proposed approach with other methods
- To conduct experimental comparison
- To find balance between local and global optimization

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