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Abstract

Automated reasoning tasks in many real-world domains involve analysis of redundancies in unsatisfiable instances of SAT. In CNF-based instances, some of the redundancies can be captured by computing a minimally unsatisfiable subset of clauses (MUS). However, the notion of MUS does not apply directly to non-clausal instances of SAT, particularly those that are represented as Boolean circuits. In this paper we identify certain types of redundancies in unsatisfiable Boolean circuits, and propose a number of algorithms to compute minimally unsatisfiable, that is, irredundant, subcircuits.

Keywords

Propositional Formula Satisfying Assignment Boolean Circuit Input Gate Output Gate 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Biere, A.: Picosat essentials. Journal on Satisfiability, Boolean Modeling and Computation 4, 75–97 (2008)zbMATHGoogle Scholar
  2. 2.
    Desrosiers, C., Galinier, P., Hertz, A., Paroz, S.: Using heuristics to find minimal unsatisfiable subformulas in satisfiability problems. J. Comb. Optim. 18(2), 124–150 (2009)CrossRefzbMATHGoogle Scholar
  3. 3.
    Grégoire, É., Mazure, B., Piette, C.: On approaches to explaining infeasibility of sets of Boolean clauses. In: Int’l. Conf. on Tools with Artificial Intelligence, pp. 74–83 (2008)Google Scholar
  4. 4.
    Jain, H., Clarke, E.M.: Efficient SAT solving for non-clausal formulas using DPLL, graphs, and watched cuts. In: Proc. of the 46th Annual Design Automation Conference, pp. 563–568 (2009)Google Scholar
  5. 5.
    Järvisalo, M., Le Berre, D., Roussel, O.: Rules of the 2011 SAT Competition (2011), http://www.satcompetition.org/2011/
  6. 6.
    Kleine Büuning, H., Kullmann, O.: Minimal unsatisfiability and autarkies. In: Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.) Handbook of Satisfiability, ch. 11, pp. 339–401. IOS Press, Amsterdam (2009)Google Scholar
  7. 7.
    Le Berre, D., Parrain, A.: The Sat4j library, release 2.2. Journal on Satisfiability, Boolean Modeling and Computation 7, 59–64 (2010)Google Scholar
  8. 8.
    Marques-Silva, J.: Minimal unsatisfiability: Models, algorithms and applications. In: Int’l Symposium on Multiple-Valued Logic, pp. 9–14 (2010)Google Scholar
  9. 9.
    Marques-Silva, J., Lynce, I.: On improving MUS extraction algorithms. In: Sakallah, K.A., Simon, L. (eds.) SAT 2011. LNCS, vol. 6695, pp. 156–170. Springer, Heidelberg (2011)Google Scholar
  10. 10.
    Nadel, A.: Boosting minimal unsatisfiable core extraction. In: Formal Methods in Computer- Aided Design (2010)Google Scholar
  11. 11.
    Schuppan, V.: Towards a notion of unsatisfiable cores for LTL. In: Fundamentals of Software Engineering. In: Third IPM Int’l Conference, pp. 129–145 (2010)Google Scholar
  12. 12.
    Tseitin, G.S.: On the complexity of derivations in the propositional calculus. Studies in Mathematics and Mathematical Logic, Part II, pp. 115–125 (1968)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Anton Belov
    • 1
  • Joao Marques-Silva
    • 1
  1. 1.Complex and Adaptive Systems Laboratory School of Computer Science and InformaticsUniversity College DublinIreland

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