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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

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checking sequence generation using state distinguishing subsequences

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
Outline
  • Problem statement
  • Previous work
  • Contribution of this work
  • Example
  • Conclusion
problem statement
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
Key Issue
  • How to recognize states in the implementation
    • State distinguishing subsequences
      • Same input, but with different outputs
    • Different distinguishing capacities
previous work
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
previous work1
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
previous work2
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)
previous work3
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)
previous work4
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
previous work5
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
previous work6
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
previous work7
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
previous work8
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
previous work9
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
previous work10
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
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 work1
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
example1
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
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
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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