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Safety and Liveness Properties for Real Traces and a Direct Translation from LTL to Monoids

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Formal and Natural Computing

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2300))

Abstract

For infinite words there are well-known characterizations of safety and liveness properties. We extend these results to real Mazurkiewicz traces. This is possible due to a result, which has been established recently: Every first-order definable real trace language is definable in linear temporal logic using future tense operators, only. We show that the canonical choice for a topological characterization of safety and liveness properties is given by the Scott topology. In this paper we use an algebraic approach where we work with aperiodic monoids. Therefore we also give a direct translation from temporal logic to aperiodic monoids which is of independent interest.

Support of ADVANCE, CEFIPRA, and PROCOPE is gratefully acknowledged.

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References

  1. IJ. J. Aalbersberg and G. Rozenberg. Theory of Traces. Theoretical Computer Science, 60:1–82, 1988.

    Article  MATH  MathSciNet  Google Scholar 

  2. B. Alpern and F.B. Schneider. Defining Liveness. Information Processing Letters, 21:181–185, 1985.

    Article  MATH  MathSciNet  Google Scholar 

  3. B. Alpern and F.B. Schneider. Recognizing Safety and Liveness. Distributed Computing, 2:117–126, 1987.

    Article  MATH  Google Scholar 

  4. R. Alur, D. Peled, and W. Penczek. Model-Checking of Causality Properties. In Proceedings of LICS’95, pages 90–100, 1995.

    Google Scholar 

  5. E. Chang, Z. Manna, and A. Pnueli. Characterization of Temporal Property Classes. In W. Kuich, Editor, Proceedings of the 19th International Colloquium on Automata, Languages and Programming (ICALP’92), Vienna, volume 623 of Lecture Notes in Computer Science, pages 474–486, Berlin-Heidelberg-New York, 1992. Springer.

    Google Scholar 

  6. C. Choffrut. Combinatorics in Trace Monoids I. In V. Diekert and G. Rozenberg, Editors, The Book of Traces, chapter 3, pages 71–82. World Scientific, Singapore, 1995.

    Google Scholar 

  7. V. Diekert and P. Gastin. LTL Is Expressively Complete for Mazurkiewicz Traces. In U. M. et al., Editor, Proceedings of the 27th International Colloquium on Automata, Languages and Programming (ICALP’00), Geneva, number 1853 in Lecture Notes in Computer Science, pages 211–222. Springer, 2000.

    Google Scholar 

  8. V. Diekert and G. Rozenberg, Editors. The Book of Traces. World Scientific, Singapore, 1995.

    Google Scholar 

  9. W. Ebinger. Charakterisierung von Sprachklassen unendlicher Spuren durch Logiken. Dissertation, Institut für Informatik, Universität Stuttgart, 1994.

    Google Scholar 

  10. W. Ebinger and A. Muscholl. Logical Definability on Infinite Traces. Theoretical Computer Science, 154:67–84, 1996. A preliminary version appeared in Proceedings of the 20th International Colloquium on Automata, Languages and Programming (ICALP’93), Lund (Sweden) 1993, Lecture Notes in Computer Science 700, 1993.

    Google Scholar 

  11. A. Ehrenfeucht, H.J. Hoogeboom, and G. Rozenberg. Combinatorial Properties of Dependence Graphs. Information and Computation, 114(2):315–328, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  12. A. Ehrenfeucht and G. Rozenberg. On the Structure of Dependence Graphs. In K. Voss, H.J. Genrich, and G. Rozenberg, Editors, Concurrency and Nets, pages 141–170, Berlin-Heidelberg-New York, 1987. Springer.

    Google Scholar 

  13. D. Gabbay, A. Pnueli, S. Shelah, and J. Stavi. On the Temporal Analysis of Fairness. In Conference Record of the 12th ACM Symposium on Principles of Programming Languages, pages 163–173, Las Vegas, Nev., 1980.

    Google Scholar 

  14. P. Gastin and A. Petit. Infinite Traces. In V. Diekert and G. Rozenberg, Editors, The Book of Traces, chapter 11, pages 393–486. World Scientific, Singapore, 1995.

    Google Scholar 

  15. P. Gastin, A. Petit, and W. Zielonka. An Extension of Kleene’s and Ochmański’s Theorems to Infinite Traces. Theoretical Computer Science, 125:167–204, 1994. A preliminary version was presented at ICALP’91, Lecture Notes in Computer Science 510 (1991).

    Google Scholar 

  16. G. Gierz, K.H. Hofmann, K. Keimel, J.D. Lawson, M.W. Mislove, and D.S. Scott. A Compendium of Continuous Lattices. Springer, Berlin-Heidelberg-New York, 1980.

    MATH  Google Scholar 

  17. G. Guaiana, A. Restivo, and S. Salemi. Star-Free Trace Languages. Theoretical Computer Science, 97:301–311, 1992. A preliminary version was presented at STACS’91, Lecture Notes in Computer Science 480 (1991).

    Google Scholar 

  18. H.J. Hoogeboom and G. Rozenberg. Dependence Graphs. In V. Diekert and G. Rozenberg, Editors, The Book of Traces, chapter 2, pages 43–67. World Scientific, Singapore, 1995.

    Google Scholar 

  19. R.M. Keller. Parallel Program Schemata and Maximal Parallelism I. Fundamental Results. Journal of the Association for Computing Machinery, 20(3):514–537, 1973.

    MATH  MathSciNet  Google Scholar 

  20. Z. Manna and A. Pnueli. The Temporal Logic of Reactive and Concurrent Systems, Specification. Springer, 1991.

    Google Scholar 

  21. A. Mazurkiewicz. Concurrent Program Schemes and Their Interpretations. DAIMI Rep. PB 78, Aarhus University, Aarhus, 1977.

    Google Scholar 

  22. M. Mukund and P.S. Thiagarajan. Linear Time Temporal Logics over Mazurkiewicz Traces. In Proceedings of the 21th MFCS, 1996, number 1113 in Lecture Notes in Computer Science, pages 62–92. Springer, 1996.

    Google Scholar 

  23. P. Niebert. A v-calculus with Local Views for Sequential Agents. In Proceedings of the 20th MFCS, 1995, number 969 in Lecture Notes in Computer Science, pages 563–573. Springer, 1995.

    Google Scholar 

  24. W. Penczek. Temporal Logics for Trace Systems: On Automated Verification. International Journal of Foundations of Computer Science, 4:31–67, 1993.

    Article  MATH  MathSciNet  Google Scholar 

  25. R. Ramanujam. Locally Linear Time Temporal Logic. In Proceedings of LICS’96, Lecture Notes in Computer Science, pages 118–128, 1996.

    Google Scholar 

  26. G. Rozenberg. Behaviour of Elementary Net Systems. In W. Brauer, Editor, Petri Nets: Central Models and Their Properties; Advances in Petri Nets; Proceedings of an Advanced Course, Bad Honnef, 8.–19. Sept. 1986, Vol. 1, number 254 in Lecture Notes in Computer Science, pages 60–94, Berlin-Heidelberg-New York, 1986. Springer.

    Google Scholar 

  27. G. Rozenberg and P.S. Thiagarajan. Petri Nets: Basic Notions, Structure and Behaviour. Number 224 in Lecture Notes in Computer Science, pages 585–668, Berlin-Heidelberg-New York, 1986. Springer.

    Google Scholar 

  28. P.S. Thiagarajan. A Trace Based Extension of Linear Time Temporal Logic. In Proceedings of LICS’94, pages 438–447, 1994.

    Google Scholar 

  29. P.S. Thiagarajan. A Trace Consistent Subset of PTL. In Proceedings of CONCUR’95, number 962 in Lecture Notes in Computer Science, pages 438–452, 1995.

    Google Scholar 

  30. P.S. Thiagarajan and I. Walukiewicz. An Expressively Complete Linear Time Temporal Logic for Mazurkiewicz Traces. In Proceedings of LICS’97, 1997.

    Google Scholar 

  31. I. Walukiewicz. Difficult Configurations — on the Complexity of LTrL. In K. G. Larsen et al., Editors, Proceedings of the 25th International Colloquium on Automata, Languages and Programming (ICALP’98), Aalborg, number 1443 in Lecture Notes in Computer Science, pages 140–151, Berlin-Heidelberg-New York, 1998. Springer.

    Google Scholar 

  32. I. Walukiewicz. Local Logics for Traces. Journal of Automata, Languages and Combinatorics, 2001. To appear.

    Google Scholar 

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Author information

Authors and Affiliations

  1. Inst. für Informatik, Universität Stuttgart, Breitwiesenstr. 20-22, 70565, Stuttgart

    Volker Diekert

  2. LIAFA, Université Paris, 7, 2, place Jussieu, 75251, Paris Cedex 05

    Paul Gastin

Authors
  1. Volker Diekert
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  2. Paul Gastin
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Editor information

Editors and Affiliations

  1. Computer Science Department, Technical University of Munich, Arcisstraße 21, 80333, Munich, Germany

    Wilfried Brauer

  2. Computer Science Department, Technical University of Berlin, Franklinstraße 28/29, 10587, Berlin, Germany

    Hartmut Ehrig

  3. Department of Mathematics, University of Turku, 20014, Turku, Finland

    Juhani Karhumäki

  4. Turku Centre for Computer Science, Lemminkäisenkatu 14A, 20520, Turku, Finland

    Arto Salomaa

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© 2002 Springer-Verlag Berlin Heidelberg

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Diekert, V., Gastin, P. (2002). Safety and Liveness Properties for Real Traces and a Direct Translation from LTL to Monoids. In: Brauer, W., Ehrig, H., Karhumäki, J., Salomaa, A. (eds) Formal and Natural Computing. Lecture Notes in Computer Science, vol 2300. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45711-9_2

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  • DOI: https://doi.org/10.1007/3-540-45711-9_2

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-43190-9

  • Online ISBN: 978-3-540-45711-4

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