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FPsolve: A Generic Solver for Fixpoint Equations over Semirings

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Implementation and Application of Automata (CIAA 2014)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8587))

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Abstract

We introduce FPsolve, an implementation of generic algorithms for solving fixpoint equations over semirings. We first illustrate the interest of generic solvers by means of a scenario. We then succinctly describe some of the algorithms implemented in the tool, and provide some implementation details.

This work was funded by the DFG project “Polynomial Systems on Semirings: Foundations, Algorithms, Applications”.

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References

  1. Goblint, http://goblint.in.tum.de/

  2. WALi: The Weighted Automata Library, https://research.cs.wisc.edu/wpis/wpds/

  3. Weighted Pushdown Systems Library, http://www2.informatik.uni-stuttgart.de/fmi/szs/tools/wpds/

  4. Apinis, K., Seidl, H., Vojdani, V.: How to combine widening and narrowing for non-monotonic systems of equations. In: Boehm, H.J., Flanagan, C. (eds.) PLDI, pp. 377–386. ACM (2013)

    Google Scholar 

  5. Bouajjani, A., Esparza, J., Schwoon, S., Suwimonteerabuth, D.: SDSIrep: A Reputation System Based on SDSI. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 501–516. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  6. Bouajjani, A., Esparza, J., Touili, T.: A generic approach to the static analysis of concurrent programs with procedures. Int. J. Found. Comput. Sci. 14(4), 551 (2003)

    Article  MATH  MathSciNet  Google Scholar 

  7. Droste, M., Kuich, W., Vogler, H.: Handbook of Weighted Automata. Springer (2009)

    Google Scholar 

  8. Esparza, J., Kiefer, S., Luttenberger, M.: On Fixed Point Equations over Commutative Semirings. In: Thomas, W., Weil, P. (eds.) STACS 2007. LNCS, vol. 4393, pp. 296–307. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  9. Esparza, J., Kiefer, S., Luttenberger, M.: Newtonian Program Analysis. J. ACM 57(6), 33 (2010)

    Article  MathSciNet  Google Scholar 

  10. Esparza, J., Luttenberger, M.: Solving fixed-point equations by derivation tree analysis. In: Corradini, A., Klin, B., Cîrstea, C. (eds.) CALCO 2011. LNCS, vol. 6859, pp. 19–35. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  11. Green, T.J., Karvounarakis, G., Tannen, V.: Provenance semirings. In: PODS, pp. 31–40 (2007)

    Google Scholar 

  12. Jha, S., Reps, T.W.: Model checking SPKI/SDSI. Journal of Computer Security 12(3-4), 317–353 (2004)

    Google Scholar 

  13. Knoop, J., Steffen, B.: The interprocedural coincidence theorem. In: Pfahler, P., Kastens, U. (eds.) CC 1992. LNCS, vol. 641, pp. 125–140. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  14. Kuich, W.: Semirings and Formal Power Series: Their Relevance to Formal Languages and Automata. In: Handbook of Formal Languages, ch. 9, vol. 1, pp. 609–677. Springer (1997)

    Google Scholar 

  15. Luttenberger, M., Schlund, M.: Convergence of Newton’s Method over Commutative Semirings. In: Dediu, A.-H., Martín-Vide, C., Truthe, B. (eds.) LATA 2013. LNCS, vol. 7810, pp. 407–418. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  16. Reps, T., Schwoon, S., Jha, S., Melski, D.: Weighted pushdown systems and their application to interprocedural dataflow analysis. Science of Computer Programming 58(1-2), 206–263 (2003); Special Issue on the Static Analysis Symposium 2003

    Google Scholar 

  17. Schlund, M., Terepeta, M., Luttenberger, M.: Putting Newton into Practice: A Solver for Polynomial Equations over Semirings. In: McMillan, K., Middeldorp, A., Voronkov, A. (eds.) LPAR-19 2013. LNCS, vol. 8312, pp. 727–734. Springer, Heidelberg (2013)

    Chapter  Google Scholar 

  18. Steffen, B., Claßen, A., Klein, M., Knoop, J., Margaria, T.: The fixpoint-analysis machine. In: Lee, I., Smolka, S.A. (eds.) CONCUR 1995. LNCS, vol. 962, pp. 72–87. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

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Esparza, J., Luttenberger, M., Schlund, M. (2014). FPsolve: A Generic Solver for Fixpoint Equations over Semirings. In: Holzer, M., Kutrib, M. (eds) Implementation and Application of Automata. CIAA 2014. Lecture Notes in Computer Science, vol 8587. Springer, Cham. https://doi.org/10.1007/978-3-319-08846-4_1

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  • DOI: https://doi.org/10.1007/978-3-319-08846-4_1

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-08845-7

  • Online ISBN: 978-3-319-08846-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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