Skip to main content
Log in

Distributed state space minimization

  • Regular contribution
  • Published:
International Journal on Software Tools for Technology Transfer Aims and scope Submit manuscript

Abstract

We present a new algorithm, and its distributed implementation, for reducing labeled transition systems modulo strong bisimulation. The base of this algorithm is the Kanellakis–Smolka “naive method”, which has a high theoretical complexity but is successful in practice and well suited to parallelization. This basic approach is combined with optimizations inspired by the Kanellakis–Smolka algorithm for the case of bounded fanout, which has the best known time complexity. The distributed implementation is improved with respect to previous attempts by a better overlap between communication and computation, which results in an efficient usage of both memory and processing power. We also discuss the time complexity of this algorithm and show experimental results with sequential and distributed prototype tools.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Barnat J, Brim L, Stříbrná J (2001) Distributed LTL model-checking in SPIN. In: Proceedings SPIN’01. Lecture notes in computer science, vol 2057. Springer, Berlin Heidelberg New York, pp 200–216

  2. Behrmann G, Hune T, Vaandrager FW (2000) Distributed timed model checking – how the search order matters. In: Proceedings CAV’00. Lecture notes in computer science, vol 1855. Springer, Berlin Heidelberg New York, pp 216–231

  3. Berry G, Comon H, Finkel A (eds) (2001) Proceedings CAV’01. Lecture notes in computer science, vol 2102. Springer, Berlin Heidelberg New York

  4. Blom SCC, Fokkink WJ, Groote JF, van Langevelde I, Lisser B, van de Pol JC (2001) μCRL: a toolset for analysing algebraic specifications. In: Proceedings CAV’01. Lecture notes in computer science, vol 2102. Springer, Berlin Heidelberg New York, pp 250–254

  5. Blom SCC, Orzan SM (2002) A distributed algorithm for strong bisimulation reduction of state spaces. In: Proceedings PDMC’02. Electronic notes in theoretical computer science, vol 68

  6. CWI/SEN2, INRIA/VASY. The VLTS benchmark. http://www.inrialpes.fr/vasy/cadp/resources/benchmark_bcg.html

  7. Fernandez J-C, Mounier L (1990) Verifying bisimulations “on the fly”. In: Proceedings FORTE’90

  8. Garavel H, Mounier L (1997) Specification and verification of various distributed leader election algorithms for unidirection ring networks. Sci Comput Programm 29(1–2):171–197

  9. van Glabbeek RJ, Weijland WP (1996) Branching time and abstraction in bisimulation semantics. J ACM 43(3):555–600

    Article  MathSciNet  Google Scholar 

  10. Groote JF, Pang J, Wouters AG (2003) Analyzing a distributed system for lifting trucks. J Logic Algebr Programm 55(1–2):21–56

  11. Grumberg O, Heyman T, Schuster A (2001) Distributed symbolic model checking for μ-calculus. In: Berry G, Comon H, Finkel A (eds) [3], pp 350–362

  12. Hopcroft JE (1971) An n log n algorithm for minimizing the states in a finite automaton. In: The theory of machines and computations. Academic, New York, pp 189–196

  13. Joubert C, Mateescu R (2004) Distributed on-the-fly equivalence checking. In: Proceedings PDMC’04. Electronic notes in theoretical computer science (in press)

  14. Kanellakis PC, Smolka SA (1983) CCS expressions, finite state processes and three problems of equivalence. In: Proceedings 2nd annual ACM symposium on principles of distributed computing, pp 228–240

  15. Lerda F, Sisto R (1999) Distributed-memory model checking with SPIN. In: Proceedings SPIN’00. Lecture notes in computer science, vol 1680. Springer, Berlin Heidelberg New York

  16. Leucker M, Noll T (2001) Truth/SLC – a parallel verification platform for concurrent systems. In: Berry G, Comon H, Finkel A (eds) [3], pp 255–259

  17. Luttik SP (1997) Description and formal specification of the Link Layer of P1394. In: Proceedings 2nd international workshop on applied formal methods in system design

  18. Mateescu R (2003) A generic on-the-fly solver for alternation-free boolean equation systems. In: Proceedings TACAS’01. Lecture notes in computer science, vol 2619. Springer, Berlin Heidelberg New York, pp 81–96

  19. Paige R, Tarjan R (1987) Three partition refinement algorithms. SIAM J Comput 16(6):973–989

    Article  MathSciNet  Google Scholar 

  20. Pang J, Fokkink WJ, Hofman R, Veldema R (2003) Model checking a cache coherence protocol for a Java DSM implementation. In: Proceedings FMPPTA’03

  21. van de Pol JC, Valero Espada M (2003) Verification of JavaSpaces parallel programs. In: Proceedings ACSD’03, pp 196–205

  22. Rajasekaran S, Lee I (1998) Parallel algorithms for relational coarsest partition problems. IEEE Trans Parallel Distrib Syst 9(7):687–699

    Article  Google Scholar 

  23. Romijn JMT (2001) A timed verification of the ieee 1394 leader election protocol. Formal Methods Syst Des 19(2):165–194

    Article  Google Scholar 

  24. Stern U, Dill D (1997) Parallelizing the Murφ verifier. In: Proceedings CAV’97. Lecture notes in computer science, vol 1254. Springer, Berlin Heidelberg New York, pp 256–278

  25. Zhang S, Smolka SA (1993) Towards efficient parallelization of equivalence checking algorithms. In: Proceedings FORTE’92. IFIP Trans C-10:133–146

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Stefan Blom.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Blom, S., Orzan, S. Distributed state space minimization. Int J Softw Tools Technol Transfer 7, 280–291 (2005). https://doi.org/10.1007/s10009-004-0185-2

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10009-004-0185-2

Keywords

Navigation