Skip to main content
SpringerLink
Log in
Book cover

Advanced Logic Synthesis pp 151–168Cite as

Analysis of Incomplete Circuits Using Dependency Quantified Boolean Formulas

  • Chapter
  • First Online:

Abstract

We consider Dependency Quantified Boolean Formulas (DQBFs), a generalization of Quantified Boolean Formulas (QBFs), and demonstrate that DQBFs are a natural calculus to exactly express the realizability problem of incomplete combinational and sequential circuits with an arbitrary number of (combinational or bounded-memory) black boxes. In contrast to usual approaches for controller synthesis, restrictions to the interfaces of missing circuit parts in distributed architectures are strictly taken into account. We present a solution method for DQBFs together with the extraction of Skolem functions for existential variables, which can directly serve as implementations for the black boxes. First experimental results are provided.

This is a preview of subscription content, log in via an institution.

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   84.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   109.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info
Hardcover Book
USD   109.99
Price excludes VAT (USA)
  • Durable hardcover edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Notes

  1. 1.

    See http://www.kr.tuwien.ac.at/events/qbfgallery2013/.

References

  1. P. Ashar, M.K. Ganai, A. Gupta, F. Ivancic, Z. Yang, Efficient SAT-based bounded model checking for software verification, in International Symposium on Leveraging Applications of Formal Methods (ISoLA), ed. by T. Margaria, B. Steffen, A. Philippou, M. Reitenspieß, Technical Report, Paphos, Cyprus, vol. TR-2004-6 (Department of Computer Science, University of Cyprus, 2004), pp. 157–164

    Google Scholar 

  2. V. Balabanov, H.-J. Katherine Chiang, J.-H.R. Jiang, Henkin quantifiers and Boolean formulae: a certification perspective of DQBF. Theor. Comput. Sci. 523, 86–100 (2014)

    Article  MATH  MathSciNet  Google Scholar 

  3. A. Biere, A. Cimatti, E.M. Clarke, O. Strichman, Y. Zhu, Bounded model checking. Adv. Comput. 58, 117–148 (2003)

    Article  Google Scholar 

  4. R. Bloem, R. Könighofer, M. Seidl, SAT-based synthesis methods for safety specs, in Proceedings of VMCAI, ed. by K.L. McMillan, X. Rival. Lecture Notes in Computer Science, San Diego, CA, vol. 8318 (Springer, Berlin, 2014 ), pp. 1–20

    Google Scholar 

  5. R. Bloem, U. Egly, P. Klampfl, R. Könighofer, F. Lonsing, M. Seidl, Satisfiability-based methods for reactive synthesis from safety specifications. CoRR, abs/1604.06204 (2016), http://arxiv.org/abs/1604.06204

  6. R.K. Brayton, A. Mishchenko, ABC: an academic industrial-strength verification tool, in Proceedings of CAV, ed. by T. Touili, B. Cook, P. Jackson. Lecture Notes in Computer Science, Edinburgh, vol. 6174 (Springer, Berlin, 2010), pp. 24–40

    Google Scholar 

  7. U. Bubeck, Model-based transformations for quantified Boolean formulas. PhD thesis, University of Paderborn (2010)

    Google Scholar 

  8. U. Bubeck, H. Kleine Büning, Dependency quantified Horn formulas: models and complexity, in Proceedings of SAT, ed. by A. Biere, C.P. Gomes. Lecture Notes in Computer Science, Seattle, WA, vol. 4121 (Springer, Berlin, 2006), pp. 198–211

    Google Scholar 

  9. E.M. Clarke, A. Biere, R. Raimi, Y. Zhu, Bounded model checking using satisfiability solving. Formal Methods Syst. Des. 19(1), 7–34 (2001)

    Article  MATH  Google Scholar 

  10. S.A. Cook, The complexity of theorem-proving procedures, in Proceedings of STOC (ACM, New York, 1971), pp. 151–158

    Google Scholar 

  11. A. Czutro, I. Polian, M.D.T. Lewis, P. Engelke, S.M. Reddy, B. Becker, Thread-parallel integrated test pattern generator utilizing satisfiability analysis. Int. J. Parallel Prog. 38(3–4),185–202 (2010)

    Article  MATH  Google Scholar 

  12. W. Damm, B. Finkbeiner, Automatic compositional synthesis of distributed systems, in Proceedings of FM, ed. by C.B. Jones, P. Pihlajasaari, J. Sun. Lecture Notes in Computer Science, Singapore, vol. 8442 (Springer, Berlin, 2014), pp. 179–193

    Google Scholar 

  13. S. Eggersglüß, R. Drechsler, A highly fault-efficient SAT-based ATPG flow. IEEE Des. Test Comput. 29(4), 63–70 (2012)

    Article  Google Scholar 

  14. B. Finkbeiner, S. Schewe, Bounded synthesis. Int. J. Softw. Tools Technol. Transfer 15(5–6), 519–539 (2013)

    Article  MATH  Google Scholar 

  15. B. Finkbeiner, L. Tentrup, Fast DQBF refutation, in Proceedings of SAT, ed. by C. Sinz, U. Egly. Lecture Notes in Computer Science, Vienna, vol. 8561 (Springer, Berlin, 2014), pp. 243–251

    Google Scholar 

  16. A. Fröhlich, G. Kovásznai, A. Biere, A DPLL algorithm for solving DQBF, in International Workshop on Pragmatics of SAT (POS), Trento (2012)

    Google Scholar 

  17. A. Fröhlich, G. Kovásznai, A. Biere, H. Veith, iDQ: instantiation-based DQBF solving, in International Workshop on Pragmatics of SAT (POS), ed. by D. Le Berre. EPiC Series, Vienna, vol. 27 ( EasyChair, 2014), pp. 103–116

    Google Scholar 

  18. K. Gitina, S. Reimer, M. Sauer, R. Wimmer, C. Scholl, B. Becker, Equivalence checking for partial implementations revisited, in Proceedings of MBMV, ed. by C. Haubelt, D. Timmermann, Rostock (Universität Rostock, ITMZ, 2013), pp. 61–70

    Google Scholar 

  19. K. Gitina, S. Reimer, M. Sauer, R. Wimmer, C. Scholl, B. Becker, Equivalence checking of partial designs using dependency quantified Boolean formulae, in Proceedings of ICCD, Asheville, NC (IEEE CS, 2013), pp. 396–403

    Google Scholar 

  20. K. Gitina, R. Wimmer, S. Reimer, M. Sauer, C. Scholl, B. Becker, Solving DQBF through quantifier elimination, in Proceedings of DATE, Grenoble (IEEE, New York, 2015)

    Google Scholar 

  21. M. Herbstritt, B. Becker, C. Scholl, Advanced SAT-techniques for bounded model checking of blackbox designs, in Proceedings of MTV (IEEE, New York, 2006), pp. 37–44

    Google Scholar 

  22. F. Lonsing, A. Biere, DepQBF: a dependency-aware QBF solver. J. Satisf. Boolean Model. Comput. 7(2–3), 71–76 (2010)

    Google Scholar 

  23. F. Lonsing, F. Bacchus, A. Biere, U. Egly, M. Seidl, Enhancing search-based QBF solving by dynamic blocked clause elimination, in Proceedings of LPAR, ed. by M. Davis, A. Fehnker, A. McIver, A. Voronkov. Lecture Notes in Computer Science, Suva, vol. 9450 (Springer, Berlin, 2015), pp. 418–433

    Google Scholar 

  24. K.L. McMillan, Applications of Craig interpolants in model checking, in Proceedings of TACAS, ed. by N. Halbwachs, L.D. Zuck. Lecture Notes in Computer Science, Edinburgh, vol. 3440 (Springer, Berlin, 2005), pp. 1–12

    Google Scholar 

  25. T. Nopper, C. Scholl, Symbolic model checking for incomplete designs with flexible modeling of unknowns. IEEE Trans. Comput. 62(6), 1234–1254 (2013)

    Article  MATH  MathSciNet  Google Scholar 

  26. G. Peterson, J. Reif, S. Azhar, Lower bounds for multiplayer non-cooperative games of incomplete information. Comput. Math. Appl. 41(7–8), 957–992 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  27. F. Pigorsch, C. Scholl, Exploiting structure in an AIG based QBF solver, in Proceedings of DATE (IEEE, New York, 2009), pp. 1596–1601

    Google Scholar 

  28. A. Pnueli, R. Rosner, Distributed reactive systems are hard to synthesize, in Annual Symposium on Foundations of Computer Science, St. Louis, MO (IEEE Computer Society, Washington, 1990), pp. 746–757

    Google Scholar 

  29. C. Scholl, B. Becker, Checking equivalence for partial implementations, in Proceedings of DAC, Las Vegas, NV (ACM, New York, 2001), pp. 238–243

    Google Scholar 

  30. C.-J.H. Seger, R.E. Bryant, Formal verification by symbolic evaluation of partially-ordered trajectories. Formal Methods Syst. Des. 6(2), 147–189 (1995)

    Article  Google Scholar 

  31. C.-J.H. Seger, R.B. Jones, J.W. O’Leary, T.F. Melham, M. Aagaard, C. Barrett, D. Syme, An industrially effective environment for formal hardware verification. IEEE Trans. CAD Integr. Circuits Syst. 24(9), 1381–1405 (2005)

    Article  Google Scholar 

  32. G.S. Tseitin, On the complexity of derivation in propositional calculus, in Studies in Constructive Mathematics and Mathematical Logic Part 2 (Springer, Berlin, 1970), pp. 115–125

    Google Scholar 

  33. R. Wimmer, K. Gitina, J. Nist, C. Scholl, B. Becker, Preprocessing for DQBF, in Proceedings of SAT, ed. by M. Heule, S. Weaver. Lecture Notes in Computer Science, Austin, TX, vol. 9340 (Springer, Berlin, 2015), pp. 173–190

    Google Scholar 

  34. K. Wimmer, R. Wimmer, C. Scholl, B. Becker, Skolem functions for DQBF, in Proceedings of ATVA, Lecture Notes in Computer Science, Chiba, vol. 9938 (Springer, Berlin, 2016), pp. 395–411

    Google Scholar 

  35. K. Wimmer, R. Wimmer, C. Scholl, B. Becker, Skolem functions for DQBF (extended version). Technical Report, FreiDok, Freiburg im Breisgau (2016), https://www.freidok.uni-freiburg.de/data/11130

    MATH  Google Scholar 

  36. R. Wimmer, S. Reimer, P. Marin, B. Becker, HQSpre–an effective preprocessor for QBF and DQBF, in Proceedings of TACAS, Part I, ed. by A. Legay, T. Margaria. Lecture Notes in Computer Science, Uppsala, vol. 10205 (Springer, Berlin, 2017)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Computer Science, Albert-Ludwigs-Universität Freiburg, Freiburg im Breisgau, Germany

    Ralf Wimmer, Karina Wimmer, Christoph Scholl & Bernd Becker

Authors
  1. Ralf Wimmer
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Karina Wimmer
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Christoph Scholl
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Bernd Becker
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Ralf Wimmer .

Editor information

Editors and Affiliations

  1. PPGC/PGMICRO, Institute of Informatics, UFRGS, Porto Alegre, Rio Grande do Sul, Brazil

    André Inácio Reis

  2. Group for Computer Architecture, University of Bremen, Bremen, Germany

    Rolf Drechsler

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG

About this chapter

Check for updates. Verify currency and authenticity via CrossMark

Cite this chapter

Wimmer, R., Wimmer, K., Scholl, C., Becker, B. (2018). Analysis of Incomplete Circuits Using Dependency Quantified Boolean Formulas. In: Reis, A., Drechsler, R. (eds) Advanced Logic Synthesis. Springer, Cham. https://doi.org/10.1007/978-3-319-67295-3_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-67295-3_7

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67294-6

  • Online ISBN: 978-3-319-67295-3

  • eBook Packages: EngineeringEngineering (R0)

Publish with us

Policies and ethics

Search

Navigation