Bounded Cycle Synthesis

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9779)

Abstract

We introduce a new approach for the synthesis of Mealy machines from specifications in linear-time temporal logic (LTL), where the number of cycles in the state graph of the implementation is limited by a given bound. Bounding the number of cycles leads to implementations that are structurally simpler and easier to understand. We solve the synthesis problem via an extension of SAT-based bounded synthesis, where we additionally construct a witness structure that limits the number of cycles. We also establish a triple-exponential upper and lower bound for the potential blow-up between the length of the LTL formula and the number of cycles in the state graph.

References

  1. 1.
    Alur, R., La Torre, S.: Deterministic generators and games for LTL fragments. ACM Trans. Comput. Log. 5(1), 1–25 (2004). http://doi.acm.org/10.1145/963927.963928 MathSciNetCrossRefGoogle Scholar
  2. 2.
    ARM Ltd.: AMBA Specification (rev. 2) (1999). www.arm.com
  3. 3.
    Babiak, T., Křetínský, M., Řehák, V., Strejček, J.: LTL to Büchi automata translation: fast and more deterministic. In: Flanagan, C., König, B. (eds.) TACAS 2012. LNCS, vol. 7214, pp. 95–109. Springer, Heidelberg (2012). http://dx.doi.org/10.1007/978-3-642-28756-5_8 CrossRefGoogle Scholar
  4. 4.
    Bloem, R., Chatterjee, K., Henzinger, T.A., Jobstmann, B.: Better quality in synthesis through quantitative objectives. In: Bouajjani, A., Maler, O. (eds.) CAV 2009. LNCS, vol. 5643, pp. 140–156. Springer, Heidelberg (2009). http://dx.doi.org/10.1007/978-3-642-02658-4_14 CrossRefGoogle Scholar
  5. 5.
    Eén, N., Sörensson, N.: An extensible SAT-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004). http://dx.doi.org/10.1007/978-3-540-24605-3_37 CrossRefGoogle Scholar
  6. 6.
    Filiot, E., Jin, N., Raskin, J.: Antichains and compositional algorithms for LTL synthesis. Form. Methods Syst. Des. 39(3), 261–296 (2011). http://dx.doi.org/10.1007/s10703-011-0115-3 CrossRefMATHGoogle Scholar
  7. 7.
    Filiot, E., Jin, N., Raskin, J.: Exploiting structure in LTL synthesis. STTT 15(5–6), 541–561 (2013). http://dx.doi.org/10.1007/s10009-012-0222-5 CrossRefGoogle Scholar
  8. 8.
    Finkbeiner, B., Klein, F.: Bounded cycle synthesis. CoRR abs/1605.01511 (2016). http://arxiv.org/abs/1605.01511
  9. 9.
    Finkbeiner, B., Schewe, S.: Bounded synthesis. STTT 15(5–6), 519–539 (2013). http://dx.doi.org/10.1007/s10009-012-0228-z CrossRefMATHGoogle Scholar
  10. 10.
    Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: clasp: a conflict-driven answer set solver. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 260–265. Springer, Heidelberg (2007). http://dx.doi.org/10.1007/978-3-540-72200-7_23 CrossRefGoogle Scholar
  11. 11.
    Jacobs, S., Klein, F.: A high-level LTL synthesis format: TLSF v1.1 (Extended Version). CoRR abs/1604.02284 (2016). http://arxiv.org/abs/1604.02284
  12. 12.
    Jobstmann, B.: Applications and optimizations for LTL synthesis. Ph.D. thesis, Graz University of Technology, March 2007Google Scholar
  13. 13.
    Johnson, D.B.: Finding all the elementary circuits of a directed graph. SIAM J. Comput. 4(1), 77–84 (1975). http://dx.doi.org/10.1137/0204007 MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Kupferman, O.: Recent challenges and ideas in temporal synthesis. In: Bieliková, M., Friedrich, G., Gottlob, G., Katzenbeisser, S., Turán, G. (eds.) SOFSEM 2012. LNCS, vol. 7147, pp. 88–98. Springer, Heidelberg (2012). doi:10.1007/978-3-642-27660-6_8 CrossRefGoogle Scholar
  15. 15.
    Kupferman, O., Vardi, M.Y.: Safraless decision procedures. In: 46th Annual IEEE Symposium on Foundations of Computer Science (FOCS 2005), 23–25 October 2005, Pittsburgh, PA, USA, Proceedings, pp. 531–542. IEEE Computer Society (2005). http://dx.doi.org/10.1109/SFCS.2005.66
  16. 16.
    Piterman, N.: From nondeterministic Büchi and Streett automata to deterministic parity automata. Log. Methods Comput. Sci. 3(3) (2007). http://dx.doi.org/10.2168/LMCS-3(3:5)2007
  17. 17.
    Tiernan, J.C.: An efficient search algorithm to find the elementary circuits of a graph. Commun. ACM 13(12), 722–726 (1970). http://doi.acm.org/10.1145/362814.362819 MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Weinblatt, H.: A new search algorithm for finding the simple cycles of a finite directed graph. J. ACM 19(1), 43–56 (1972). http://doi.acm.org/10.1145/321679.321684 MathSciNetCrossRefMATHGoogle Scholar

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Reactive Systems GroupSaarland UniversitySaarbrückenGermany

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