Skip to main content
SpringerLink
Log in
Book cover

International Conference on Developments in Language Theory

DLT 2015: Developments in Language Theory pp 413–425Cite as

Weight Assignment Logic

  • Conference paper
  • First Online:

  • 530 Accesses

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9168))

Abstract

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.

Supported by DFG Research Training Group 1763 (QuantLA).

This is a preview of subscription content, 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   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
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

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Andersson, D.: Improved combinatorial algorithms for discounted payoff games. Master’s thesis, Uppsala University, Department of Information Technology (2006)

    Google Scholar 

  2. Bloem, R., Greimel, K., Henzinger, T.A., Jobstmann, B.: Synthesizing robust systems. In: FMCAD 2009, pp. 85–92. IEEE (2009)

    Google Scholar 

  3. Bouyer, P.: A logical characterization of data languages. Inf. Process. Lett. 84(2), 75–85 (2002)

    Article  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  5. Büchi, J.R.: Weak second-order arithmetic and finite automata. Z. Math. Logik und Grundl. Math. 6, 66–92 (1960)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  8. Droste, M., Gastin, P.: Weighted automata and weighted logics. Theoret. Comp. Sci. 380(1–2), 69–86 (2007)

    Article  MathSciNet  Google Scholar 

  9. Droste, M., Kuich, W., Vogler, H. (eds.): Handbook of Weighted Automata. EATCS Monographs on Theoretical Computer Science. Springer (2009)

    Google Scholar 

  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. Droste, M., Meinecke, I.: Weighted automata and weighted MSO logics for average and long-time behaviors. Inf. Comput. 220–221, 44–59 (2012)

    Article  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

  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. 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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Chapter  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Article  MathSciNet  Google Scholar 

  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)

    Chapter  Google Scholar 

  20. Nivat, M.: Transductions des langages de Chomsky. Ann. de l’Inst. Fourier 18, 339–456 (1968)

    Article  MathSciNet  Google Scholar 

  21. Stüber, T., Vogler, H., Fülöp, Z.: Decomposition of weighted multioperator tree automata. Int. J. Foundations of Computer Sci. 20(2), 221–245 (2009)

    Article  Google Scholar 

  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)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institut für Informatik, Universität Leipzig, 04109, Leipzig, Germany

    Vitaly Perevoshchikov

Authors
  1. Vitaly Perevoshchikov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Vitaly Perevoshchikov .

Editor information

Editors and Affiliations

  1. University of Liverpool, Liverpool, United Kingdom

    Igor Potapov

Rights and permissions

Reprints and permissions

Copyright information

© 2015 Springer International Publishing Switzerland

About this paper

Cite this paper

Perevoshchikov, V. (2015). Weight Assignment Logic. In: Potapov, I. (eds) Developments in Language Theory. DLT 2015. Lecture Notes in Computer Science(), vol 9168. Springer, Cham. https://doi.org/10.1007/978-3-319-21500-6_33

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-21500-6_33

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21499-3

  • Online ISBN: 978-3-319-21500-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation