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MSO logics for weighted timed automata

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Abstract

We aim to generalize Büchi’s fundamental theorem on the coincidence of recognizable and MSO-definable languages to a weighted timed setting. For this, we investigate weighted timed automata and show how we can extend Wilke’s relative distance logic with weights taken from an arbitrary semiring. We show that every formula in our logic can effectively be transformed into a weighted timed automaton, and vice versa. The results indicate the robustness of weighted timed automata and may also be used for specification purposes.

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References

  1. Alur R, Dill DL (1994) A theory of timed automata. Theor Comput Sci 126(2):183–235

    Article  MATH  MathSciNet  Google Scholar 

  2. Alur R, La Torre S, Pappas GJ (2004) Optimal paths in weighted timed automata. Theor Comput Sci 318:297–322

    Article  MATH  MathSciNet  Google Scholar 

  3. Alur R, Madhusudan P (2004) Decision problems for timed automata: A survey. In: Bernardo M, Corradini F (eds) SFM-RT. LNCS, vol 3185. Springer, Berlin, pp 1–24

    Google Scholar 

  4. Behrmann G, Fehnker A, Hune T, Larsen K, Pettersson P, Romijn J, Vaandrager F (2001) Minimum-cost reachability for priced timed automata. In: Di Benedetto MD, Sangiovanni-Vincentelli A (eds) HSCC. LNCS, vol 2034. Springer, Berlin, pp 147–161

    Google Scholar 

  5. Bollig B, Meinecke I (2007) Weighted distributed systems and their logics. In: Artëmov SN, Nerode A (eds) LFCS. LNCS, vol 4514. Springer, Berlin, pp 54–68

    Google Scholar 

  6. Bouyer P, Brihaye T, Bruyère V, Raskin J-F (2007) On the optimal reachability problem on weighted timed automata. Form Methods Syst Des 31(2):135–175

    Article  MATH  Google Scholar 

  7. Bouyer P, Brihaye T, Markey N (2006) Improved undecidability results on weighted timed automata. Inf Process Lett 98(5):188–194

    Article  MATH  MathSciNet  Google Scholar 

  8. Bouyer P, Larsen KG, Markey N (2008) Model checking one-clock priced timed automata. Log Methods Comput Sci 4:1–28

    MathSciNet  Google Scholar 

  9. Bouyer P, Markey N (2007) Costs are expensive! In: Raskin J-F, Thiagarajan PS (eds) FORMATS. LNCS, vol 4763. Springer, Berlin, pp 53–68

    Google Scholar 

  10. Büchi JR (1960) On a decision method in restricted second order arithmetics. In: Nagel E et al. (eds) Proc intern congress on logic, methodology and philosophy of sciences. Stanford University Press, Stanford, pp 1–11

    Google Scholar 

  11. Chiplunkar A, Narayanan Krishna S, Jain C (2009) Model checking logic WCTL with multi constrained modalities on one clock priced timed automata. In: Ouaknine J, Vaandrager FW (eds) FORMATS. LNCS, vol 5813. Springer, Berlin, pp 88–102

    Google Scholar 

  12. Droste M, Gastin P (2005) Weighted automata and weighted logics. In: Caires L, Italiano GF, Monteiro L, Palamidessi C, Yung M (eds) ICALP. LNCS, vol 3580. Springer, Berlin, pp 513–525

    Google Scholar 

  13. Droste M, Gastin P (2009) Weighted automata and weighted logics. In: Droste M, Kuich W, Vogler H (eds) Handbook of weighted automata. EATCS monographs in theoretical computer science. Springer, Berlin, pp 175–211

    Chapter  Google Scholar 

  14. Droste M, Quaas K (2008) A Kleene-Schützenberger theorem for weighted timed automata. In: Amadio RM (ed) FoSSaCS. LNCS, vol 4962. Springer, Berlin, pp 142–156

    Google Scholar 

  15. Droste M, Rahonis G (2006) Weighted automata and weighted logics on infinite words. In: Ibarra OH, Dang Z (eds) Developments in language theory. LNCS, vol 4036. Springer, Berlin, pp 49–58

    Chapter  Google Scholar 

  16. Droste M, Vogler H (2006) Weighted tree automata and weighted logics. Theor Comput Sci 366(3):228–247

    Article  MATH  MathSciNet  Google Scholar 

  17. D’Souza D (2003) A logical characterisation of event clock automata. Int J Found Comput Sci 14(4):625–640

    Article  MATH  MathSciNet  Google Scholar 

  18. Furia CA, Rossi M (2008) MTL with bounded variability: Decidability and complexity. In: Cassez F, Jard C (eds) FORMATS. LNCS, vol 5215. Springer, Berlin, pp 109–123

    Google Scholar 

  19. Mathissen C (2007) Definable transductions and weighted logics for texts. In: Harju T, Karhumäki J, Lepistö A (eds) Developments in language theory. LNCS, vol 4588. Springer, Berlin, pp 324–336

    Chapter  Google Scholar 

  20. Mathissen C (2008) Weighted logics for nested words and algebraic formal power series. In: Aceto L, Damgård I, Goldberg L Ann, Halldórsson MM, Ingólfsdóttir A, Walukiewicz I (eds) ICALP (2). LNCS, vol 5126. Springer, Berlin, pp 221–232

    Google Scholar 

  21. Mäurer I (2006) Weighted picture automata and weighted logics. In: Durand B, Thomas W (eds) STACS. LNCS, vol 3884. Springer, Berlin, pp 313–324

    Google Scholar 

  22. Meinecke I (2006) Weighted logics for traces. In: Grigoriev D, Harrison J, Hirsch EA (eds) CSR. LNCS, vol 3967. Springer, Berlin, pp 235–246

    Google Scholar 

  23. Quaas K (2009) Kleene-Schützenberger and Büchi theorems for weighted timed automata. PhD thesis, Universität Leipzig, Institut für Informatik, Abteilung Automaten und Sprachen

  24. Quaas K (2009) Weighted timed MSO logics. In: Diekert V, Nowotka D (eds) DLT 2009, Proceedings. LNCS, vol 5583. Springer, Berlin, pp 419–430

    Google Scholar 

  25. Alur R, Henzinger TA (1990) Real-time logics: complexity and expressiveness. In: Fifth annual IEEE symposium on logic in computer science. IEEE Computer Society Press, Washington, pp 390–401

    Chapter  Google Scholar 

  26. Thomas W (1990) Automata on infinite objects. In: van Leeuwen J (ed) Handbook of theoretical computer science, Volume B: Formal models and semantics (B). Elsevier and MIT Press, Amsterdam/Cambridge, pp 133–192

    Google Scholar 

  27. Thomas W (1997) Languages, automata and logic. In: Rozenberg G, Salomaa A (eds) Handbook of formal languages. Springer, Berlin, pp 389–485

    Google Scholar 

  28. Wilke T (1994) Automaten und Logiken zur Beschreibung zeitabhängiger Systeme. PhD thesis, Christian-Albrecht-Universität Kiel

  29. Wilke T (1994) Specifying timed state sequences in powerful decidable logics and timed automata. In: Langmaack H, de Roever W-P, Vytopil J (eds) Formal techniques in real-time and fault-tolerant systems, Lübeck, Germany. LNCS, vol 863. Springer, Berlin, pp 694–715

    Google Scholar 

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  1. Institut für Informatik, Universität Leipzig, 04009, Leipzig, Germany

    Karin Quaas

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  1. Karin Quaas
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Quaas, K. MSO logics for weighted timed automata. Form Methods Syst Des 38, 193–222 (2011). https://doi.org/10.1007/s10703-011-0112-6

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