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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. Problem statement Previous work

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Checking Sequence Generation Using State Distinguishing Subsequences

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  1. 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

  2. Outline • Problem statement • Previous work • Contribution of this work • Example • Conclusion

  3. 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

  4. Key Issue • How to recognize states in the implementation • State distinguishing subsequences • Same input, but with different outputs • Different distinguishing capacities

  5. 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

  6. 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

  7. 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)

  8. 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)

  9. 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

  10. 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

  11. 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

  12. 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

  13. 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

  14. 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

  15. 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

  16. 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

  17. 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

  18. Example

  19. 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

  20. 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

  21. Future work • To integrate the proposed approach with other methods • To conduct experimental comparison • To find balance between local and global optimization

  22. Thank you! Questions? adenilso@icmc.usp.br, petrenko@crim.ca

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