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Size-Change Abstraction and Max-Plus Automata

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Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 8634))

Abstract

Max-plus automata (over ℕ ∪ − ∞) are finite devices that map input words to non-negative integers or − ∞. In this paper we present (a) an algorithm allowing to compute the asymptotic behaviour of max-plus automata, and (b) an application of this technique to the evaluation of the computational time complexity of programs.

The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement no259454 and from the Vienna Science and Technology Fund (WWTF) through grant ICT12-059.

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References

  1. Ben-Amram, A.M., Vainer, M.: Bounded termination of monotonicity-constraint transition systems. CoRR, abs/1202.4281 (2012)

    Google Scholar 

  2. Colcombet, T., Daviaud, L.: Approximate comparison of distance automata. In: STACS, pp. 574–585 (2013)

    Google Scholar 

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

    Google Scholar 

  4. Hashiguchi, K.: Limitedness theorem on finite automata with distance functions. J. Comput. Syst. Sci. 24(2), 233–244 (1982)

    Article  MATH  MathSciNet  Google Scholar 

  5. Krob, D.: The equality problem for rational series with multiplicities in the tropical semiring is undecidable. Internat. J. Algebra Comput. 4(3), 405–425 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  6. Lee, C.S., Jones, N.D., Ben-Amram, A.M.: The size-change principle for program termination. In: POPL, pp. 81–92 (2001)

    Google Scholar 

  7. Manolios, P., Vroon, D.: Termination analysis with calling context graphs. In: Ball, T., Jones, R.B. (eds.) CAV 2006. LNCS, vol. 4144, pp. 401–414. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  8. Schützenberger, M.P.: On the definition of a family of automata. Information and Control 4, 245–270 (1961)

    Article  MATH  MathSciNet  Google Scholar 

  9. Simon, I.: Factorization forests of finite height. Theoretical Computer Science 72, 65–94 (1990)

    Article  MATH  MathSciNet  Google Scholar 

  10. Simon, I.: The nondeterministic complexity of a finite automaton. In: Mots. Lang. Raison. Calc., pp. 384–400. Hermès, Paris (1990)

    Google Scholar 

  11. Zuleger, F., Gulwani, S., Sinn, M., Veith, H.: Bound analysis of imperative programs with the size-change abstraction. In: Yahav, E. (ed.) SAS 2011. LNCS, vol. 6887, pp. 280–297. Springer, Heidelberg (2011)

    Google Scholar 

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Colcombet, T., Daviaud, L., Zuleger, F. (2014). Size-Change Abstraction and Max-Plus Automata. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds) Mathematical Foundations of Computer Science 2014. MFCS 2014. Lecture Notes in Computer Science, vol 8634. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-44522-8_18

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  • DOI: https://doi.org/10.1007/978-3-662-44522-8_18

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-44521-1

  • Online ISBN: 978-3-662-44522-8

  • eBook Packages: Computer ScienceComputer Science (R0)

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