Skip to main content
Springer Nature Link
Log in

Simulation Based Minimization

  • Conference paper
Automated Deduction - CADE-17 (CADE 2000)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 1831))

Included in the following conference series:

  • 550 Accesses

Abstract

This work presents a minimization algorithm. The algorithm receives a Kripke structure M and returns the smallest structure that is simulation equivalent to M. The simulation equivalence relation is weaker than bisimulation but stronger than the simulation preorder. It strongly preserves ACTL and LTL (as sub-logics of ACTL*).

We show that every structure M has a unique up to isomorphism reduced structure that is simulation equivalent to M and smallest in size.

We give a Minimizing Algorithm that constructs the reduced structure. It first constructs the quotient structure for M, then eliminates transitions to little brothers and finally deletes unreachable states.

The first step has maximal space requirements since it is based on the simulation preorder over M. To reduce these requirements we suggest the Partitioning Algorithm which constructs the quotient structure for M without ever building the simulation preorder. The Partitioning Algorithm has a better space complexity but might have worse time complexity.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Aziz, A., Shiple, T.R., Singhal, V., Sangiovanni-Vincetelly, A.L.: Formula- dependent equivalence for compositional CTL model checking. In: Dill, D.L. (ed.) CAV 1994. LNCS, vol. 818, pp. 324–337. Springer, Heidelberg (1994)

    Google Scholar 

  2. Aziz, A., Singhal, V., Swamy, G.M., Brayton, R.K.: Minimizing interacting finite state machines: A compositional approach to language containment. In: Proceedings of the International Conference on Computer Design, pp. 255–261 (1994)

    Google Scholar 

  3. Bloom, B., Paige, R.: Transformational design and implementation of new efficient solution to the ready simulation problem. Science of Computer Programming 24, 189–220 (1996)

    Article  MathSciNet  Google Scholar 

  4. Bouajjani, A., Fernandez, J.-C., Halbwachs, N.: Minimal model generation. In: Clarke, E.M., Kurshan, R.P. (eds.) Computer-Aided Verification, New York, pp. 197–203. Springer, Heidelberg (1990)

    Google Scholar 

  5. Bouali, A., de Simone, R.: Symbolic bisimulation minimisation. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 96–108. Springer, Heidelberg (1992)

    Google Scholar 

  6. Bustan, D., Grumberg, O.: Simulation based minimization. Technical Report TR #CS-2000-04, Computer Science Department, Technion, Haifa (April 2000)

    Google Scholar 

  7. Clarke, E.M., Emerson, E.A.: Synthesis of synchronization skeletons for branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131. Springer, Heidelberg (1981)

    Google Scholar 

  8. Clarke, E.M., Grumberg, O., Peled, D.A.: Model Checking. MIT press, Cambridge (1999)

    Google Scholar 

  9. Fisler, K., Vardi, M.: Bisimulation minimization in an automata-theoretic verification framework.In: FMCAD, pp. 115–132 (1998)

    Google Scholar 

  10. Grumberg, O., Long, D.E.: Model checking and modular verification. ACM Trans. on Programming Languages and Systems 16(3), 843–871 (1994)

    Article  Google Scholar 

  11. Henzinger, M.R., Henzinger, T.A., Kopke, P.W.: Computing simulation on finite and infinite graphs. In: Proc. Symp. Foundations of Computer Science, pp. 453–462 (1995)

    Google Scholar 

  12. Kucera, A., Mayr, R.: Simulation preorder on simple process algebras. In: Wiedermann, J., Van Emde Boas, P., Nielsen, M. (eds.) ICALP 1999. LNCS, vol. 1644, p. 503. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  13. Lee, D., Yannakakis, M.: Online minimization of transition systems. In: Proceedings of the 24th ACM Symp. on Theory of Computing (1992)

    Google Scholar 

  14. Milner, R.: An algebraic definition of simulation between programs. In: Proc. of the 2nd IJCAI, London, UK, pp. 481–489 (1971)

    Google Scholar 

  15. Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104. Springer, Heidelberg (1981)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Computer Science Dept., Technion, Haifa, 32000, Israel

    Doron Bustan & Orna Grumberg

Authors
  1. Doron Bustan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Orna Grumberg
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Toyota Technological Institute at Chicago, 1427 E. 60th Street, 60637, Chicago, Illinois

    David McAllester

Rights and permissions

Reprints and permissions

Copyright information

© 2000 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Bustan, D., Grumberg, O. (2000). Simulation Based Minimization. In: McAllester, D. (eds) Automated Deduction - CADE-17. CADE 2000. Lecture Notes in Computer Science(), vol 1831. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10721959_20

Download citation

  • DOI: https://doi.org/10.1007/10721959_20

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-67664-5

  • Online ISBN: 978-3-540-45101-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics