Skip to main content
SpringerLink
Log in

Size-Change Termination and Satisfiability for Linear-Time Temporal Logics

  • Conference paper
Frontiers of Combining Systems (FroCoS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6989))

Included in the following conference series:

  • 387 Accesses

Abstract

In the automata-theoretic framework, finite-state automata are used as a machine model to capture the operational content of temporal logics. Decision problems like satisfiability, subsumption, equivalence, etc. then translate into questions on automata like emptiness, inclusion, language equivalence, etc. Linear-time temporal logics like LTL, PSL and the linear-time μ-calculus have relatively simple translations into alternating parity automata, and this automaton model is closed under all Boolean operations with very simple constructions. Thus, the typical decision problems for such linear-time temporal logics reduce relatively simply to the emptiness problem for alternating parity automata. In this paper we present a method for decision this emptiness problem without going through intermediate automaton models like nondeterministic ones. The method is a direct adaptation of the size-change termination principle which was orgininally used to decide termination of abstract functional programs.

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

Access this chapter

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 54.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 69.99
Price excludes VAT (USA)
  • Compact, lightweight 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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Abdulla, P.A., Chen, Y.-F., Clemente, L., Holík, L., Hong, C.-D., Mayr, R., Vojnar, T.: Simulation subsumption in ramsey-based büchi automata universality and inclusion testing. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 132–147. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  2. Inc. Accellera Organization. Formal semantics of Accellera property specification language (2004), In Appendix B of http://www.eda.org/vfv/docs/PSL-v1.1.pdf

  3. Banieqbal, B., Barringer, H.: Temporal logic with fixed points. In: Banieqbal, B., Pnueli, A., Barringer, H. (eds.) Temporal Logic in Specification. LNCS, vol. 398, pp. 62–73. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  4. Bustan, D., Fisman, D., Havlicek, J.: Automata constructions for PSL. Technical Report MCS05-04, The Weizmann Institute of Science (2005)

    Google Scholar 

  5. Dax, C., Hofmann, M., Lange, M.: A proof system for the linear time μ-calculus. In: Arun-Kumar, S., Garg, N. (eds.) FSTTCS 2006. LNCS, vol. 4337, pp. 274–285. Springer, Heidelberg (2006)

    Google Scholar 

  6. Dax, C., Klaedtke, F.: Alternation elimination by complementation (Extended abstract). In: Cervesato, I., Veith, H., Voronkov, A. (eds.) LPAR 2008. LNCS (LNAI), vol. 5330, pp. 214–229. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science. Formal Models and Semantics, vol. B, ch. 16, pp. 996–1072. Elsevier, MIT Press, New York, USA (1990)

    Google Scholar 

  8. Fogarty, S., Vardi, M.Y.: Büchi complementation and size-change termination. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 16–30. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  9. Fogarty, S., Vardi, M.Y.: Efficient büchi universality checking. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 205–220. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  10. Kaivola, R.: Using Automata to Characterise Fixed Point Temporal Logics. PhD thesis, LFCS, Division of Informatics, The University of Edinburgh, Tech. Rep. ECS-LFCS-97-356 (1997)

    Google Scholar 

  11. Kupferman, O., Piterman, N., Vardi, M.Y.: Extended temporal logic revisited. In: Larsen, K.G., Nielsen, M. (eds.) CONCUR 2001. LNCS, vol. 2154, pp. 519–535. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  12. Lange, M.: Linear time logics around PSL: Complexity, expressiveness, and a little bit of succinctness. In: Caires, L., Vasconcelos, V.T. (eds.) CONCUR 2007. LNCS, vol. 4703, pp. 90–104. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  13. Lee, C.S., Jones, N.D., Ben-Amram, A.M.: The size-change principle for program termination. ACM SIGPLAN Notices 36(3), 81–92 (2001)

    Article  MATH  Google Scholar 

  14. Löding, C., Thomas, W.: Alternating automata and logics over infinite words. In: Watanabe, O., Hagiya, M., Ito, T., van Leeuwen, J., Mosses, P.D. (eds.) TCS 2000. LNCS, vol. 1872, pp. 521–535. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  15. Miyano, S., Hayashi, T.: Alternating finite automata on omega-words. TCS 32(3), 321–330 (1984)

    Article  MATH  MathSciNet  Google Scholar 

  16. Pnueli, A.: The temporal logic of programs. In: Proc. 18th Symp. on Foundations of Computer Science, FOCS 1977, pp. 46–57. IEEE, Providence (1977)

    Google Scholar 

  17. Ramsey, F.P.: On a problem of formal logic. Proc. London Mathematical Society, Series 2 30(4), 338–384 (1928)

    Google Scholar 

  18. Ramsey, F.P.: On a problem in formal logic. Proc. London Math. Soc. 30(3), 264–286 (1930)

    Article  MATH  Google Scholar 

  19. Sistla, A.P., Clarke, E.M.: The complexity of propositional linear temporal logics. Journal of the Association for Computing Machinery 32(3), 733–749 (1985)

    Article  MATH  MathSciNet  Google Scholar 

  20. Stirling, C.: Comparing linear and branching time temporal logics. In: Banieqbal, B., Pnueli, A., Barringer, H. (eds.) Temporal Logic in Specification. LNCS, vol. 398, pp. 1–20. Springer, Heidelberg (1989)

    Chapter  Google Scholar 

  21. Vardi.: Linear vs. branching time: A complexity-theoretic perspective. In: LICS: IEEE Symposium on Logic in Computer Science (1998)

    Google Scholar 

  22. Vardi, M.Y.: A temporal fixpoint calculus. In: ACM (ed.) Proc. Conf. on Principles of Programming Languages, POPL 1988, pp. 250–259. ACM Press, New York (1988)

    Google Scholar 

  23. Vardi, M.Y.: Alternating automata and program verification. In: van Leeuwen, J. (ed.) Computer Science Today. LNCS, vol. 1000, pp. 471–485. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  24. Vardi, M.Y.: An Automata-Theoretic Approach to Linear Temporal Logic. In: Moller, F., Birtwistle, G. (eds.) Logics for Concurrency. LNCS, vol. 1043, pp. 238–266. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  25. Vardi, M.Y.: Branching vs. Linear time: Final showdown. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 1–22. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  26. Vardi, M.Y., Wolper, P.: Reasoning about infinite computations. Information and Computation 115(1), 1–37 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  27. Wolper, P.: Temporal logic can be more expressive. Information and Control 56, 72–99 (1983)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. School of Electr. Eng. and Computer Science, University of Kassel, Germany

    Martin Lange

Authors
  1. Martin Lange
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. University of Iowa, USA

    Cesare Tinelli

  2. Max-Planck-Institut für Informatik, Campus E 1.4, 66123, Saarbrücken, Germany

    Viorica Sofronie-Stokkermans

Rights and permissions

Reprints and permissions

Copyright information

© 2011 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Lange, M. (2011). Size-Change Termination and Satisfiability for Linear-Time Temporal Logics. In: Tinelli, C., Sofronie-Stokkermans, V. (eds) Frontiers of Combining Systems. FroCoS 2011. Lecture Notes in Computer Science(), vol 6989. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-24364-6_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-24364-6_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-24363-9

  • Online ISBN: 978-3-642-24364-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation