Weight Assignment Logic

  • Vitaly PerevoshchikovEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9168)


We introduce a weight assignment logic for reasoning about quantitative languages of infinite words. This logic is an extension of the classical MSO logic and permits to describe quantitative properties of systems with multiple weight parameters, e.g., the ratio between rewards and costs. We show that this logic is expressively equivalent to unambiguous weighted Büchi automata. We also consider an extension of weight assignment logic which is expressively equivalent to nondeterministic weighted Büchi automata.


Quantitative omega-languages Quantitative logic Multi-weighted automata Büchi automata Unambiguous automata 


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  1. 1.
    Andersson, D.: Improved combinatorial algorithms for discounted payoff games. Master’s thesis, Uppsala University, Department of Information Technology (2006)Google Scholar
  2. 2.
    Bloem, R., Greimel, K., Henzinger, T.A., Jobstmann, B.: Synthesizing robust systems. In: FMCAD 2009, pp. 85–92. IEEE (2009)Google Scholar
  3. 3.
    Bouyer, P.: A logical characterization of data languages. Inf. Process. Lett. 84(2), 75–85 (2002)MathSciNetCrossRefGoogle Scholar
  4. 4.
    Bouyer, P., Brinksma, E., Larsen, K.G.: Optimal infinite scheduling for multi-priced timed automata. Formal Methods in System Design 32, 3–23 (2008)CrossRefGoogle Scholar
  5. 5.
    Büchi, J.R.: Weak second-order arithmetic and finite automata. Z. Math. Logik und Grundl. Math. 6, 66–92 (1960)CrossRefGoogle Scholar
  6. 6.
    Chatterjee, K., Doyen, L., Henzinger, T.A.: Quantitative languages. In: Kaminski, M., Martini, S. (eds.) CSL 2008. LNCS, vol. 5213, pp. 385–400. Springer, Heidelberg (2008) CrossRefGoogle Scholar
  7. 7.
    Carton, O., Michel, M.: Unambiguous Büchi automata. In: Gonnet, G.H., Viola, A. (eds.) LATIN 2000. LNCS, vol. 1776, pp. 407–416. Springer, Heidelberg (2000) CrossRefGoogle Scholar
  8. 8.
    Droste, M., Gastin, P.: Weighted automata and weighted logics. Theoret. Comp. Sci. 380(1–2), 69–86 (2007)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Droste, M., Kuich, W., Vogler, H. (eds.): Handbook of Weighted Automata. EATCS Monographs on Theoretical Computer Science. Springer (2009)Google Scholar
  10. 10.
    Droste, M., Kuske, D.: Weighted automata. In: Pin, J.-E. (ed.) Handbook: “Automata: from Mathematics to Applications”. European Mathematical Society (to appear)Google Scholar
  11. 11.
    Droste, M., Meinecke, I.: Weighted automata and weighted MSO logics for average and long-time behaviors. Inf. Comput. 220–221, 44–59 (2012)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Droste, M., Perevoshchikov, V.: Multi-weighted automata and MSO logic. In: Bulatov, A.A., Shur, A.M. (eds.) CSR 2013. LNCS, vol. 7913, pp. 418–430. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  13. 13.
    Droste, M., Perevoshchikov, V.: A Nivat theorem for weighted timed automata and weighted relative distance logic. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014, Part II. LNCS, vol. 8573, pp. 171–182. Springer, Heidelberg (2014) Google Scholar
  14. 14.
    Droste, M., Rahonis, G.: Weighted automata and weighted logics on infinite words. In: Ibarra, O.H., Dang, Z. (eds.) DLT 2006. LNCS, vol. 4036, pp. 49–58. Springer, Heidelberg (2006) CrossRefGoogle Scholar
  15. 15.
    Fahrenberg, U., Juhl, L., Larsen, K.G., Srba, J.: Energy games in multiweighted automata. In: Cerone, A., Pihlajasaari, P. (eds.) ICTAC 2011. LNCS, vol. 6916, pp. 95–115. Springer, Heidelberg (2011) CrossRefGoogle Scholar
  16. 16.
    Filiot, E., Gentilini, R., Raskin, J.-F.: Quantitative languages defined by functional automata. In: Koutny, M., Ulidowski, I. (eds.) CONCUR 2012. LNCS, vol. 7454, pp. 132–146. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  17. 17.
    Hashiguchi, K., Ishiguro, K., Jimbo, S.: Decidability of the equivalence problem for finitely ambiguous finance automata. Int. Journal of Algebra and Computation 12(3), 445–461 (2002)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Krob, D.: The equality problem for rational series with multiplicities in the tropical semiring is undecidable. International Journal of Algebra and Computation 4(3), 405–425 (1994)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Larsen, K.G., Rasmussen, J.I.: Optimal conditional reachability for multi-priced timed automata. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 234–249. Springer, Heidelberg (2005) CrossRefGoogle Scholar
  20. 20.
    Nivat, M.: Transductions des langages de Chomsky. Ann. de l’Inst. Fourier 18, 339–456 (1968)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Stüber, T., Vogler, H., Fülöp, Z.: Decomposition of weighted multioperator tree automata. Int. J. Foundations of Computer Sci. 20(2), 221–245 (2009)CrossRefGoogle Scholar
  22. 22.
    Wilke, T.: Specifying timed state sequences in powerful decidable logics and timed automata. In: Langmaack, H., de Roever, W.-P., Vytopil, J. (eds.) FTRTFT 1994 and ProCoS 1994. LNCS, vol. 863, pp. 694–715. Springer, Heidelberg (1994) CrossRefGoogle Scholar

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© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.Institut für InformatikUniversität LeipzigLeipzigGermany

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