skip to main content
article
Open Access

The complexity of interaction

Published:11 January 2016Publication History
Skip Abstract Section

Abstract

In this paper, we analyze the complexity of functional programs written in the interaction-net computation model, an asynchronous, parallel and confluent model that generalizes linear-logic proof nets. Employing user-defined sized and scheduled types, we certify concrete time, space and space-time complexity bounds for both sequential and parallel reductions of interaction-net programs by suitably assigning complexity potentials to typed nodes. The relevance of this approach is illustrated on archetypal programming examples. The provided analysis is precise, compositional and is, in theory, not restricted to particular complexity classes.

References

  1. A. Asperti, C. Giovanetti, and A. Naletto. The bologna optimal higherorder machine. JFP, 6(6):763–810, 1996.Google ScholarGoogle ScholarCross RefCross Ref
  2. R. Atkey. Amortised resource analysis with separation logic. Logical Methods in Computer Science, 7(2), 2011.Google ScholarGoogle Scholar
  3. M. Avanzini, U. Dal Lago, and G. Moser. Analysing the complexity of functional programs: Higher-order meets first-order, 2015. Google ScholarGoogle ScholarDigital LibraryDigital Library
  4. P. Baillot and U. Dal Lago. Higher-order interpretations and program complexity. In Proc. 21th CSL, volume 16 of LIPIcs, pages 62–76, 2012.Google ScholarGoogle Scholar
  5. P.v. Emde Boas. Machine models and simulation. In Handbook of Theoretical Computer Science, Volume A: Algorithms and Complexity (A), pages 1–66. MIT Press, 1990. Google ScholarGoogle ScholarDigital LibraryDigital Library
  6. M. Brockschmidt, F. Emmes, S. Falke, C. Fuhs, and J. Giesl. Alternating runtime and size complexity analysis of integer programs. In Proc. 20th TACAS, volume 8413 of LNCS, pages 140–155, 2014.Google ScholarGoogle Scholar
  7. M. Fernández, I. Mackie, S. Sato, and M. Walker. Recursive functions with pattern matching in interaction nets. ENTCS, 253(4):55–71, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  8. D. Ghica and A. Smith. Bounded linear types in a resource semiring. In Proc. 23rd ESOP, volume 8410 of LNCS, pages 331–350, 2014.Google ScholarGoogle Scholar
  9. S. Gimenez. Programmer, calculer et raisonner avec les réseaux de la logique linéaire. PhD thesis, 2009.Google ScholarGoogle Scholar
  10. S. Gimenez and G. Moser. The complexity of interaction (long version). http://arxiv.org/abs/1511.01838.Google ScholarGoogle Scholar
  11. S. Gimenez and G. Moser. The structure of interaction. In Proc. 22nd CSL, volume 23 of LIPIcs, pages 316–331, 2013.Google ScholarGoogle Scholar
  12. J-Y. Girard, A. Scedrov, and P. Scott. Bounded linear logic: A modular approach to polynomial-time computability. TCS, 97(1):1–66, 1992. Google ScholarGoogle ScholarDigital LibraryDigital Library
  13. G. Gonthier, M. Abadi, and J.-J. Lévy. The geometry of optimal lambda reduction. In Proc. 19th POPL, pages 15–26. ACM Press, 1992. Google ScholarGoogle ScholarDigital LibraryDigital Library
  14. G. Gonthier, M. Abadi, and J.-J. Lévy. Linear logic without boxes. In Proc. 7th LICS, pages 223–234. IEEE, 1992.Google ScholarGoogle Scholar
  15. A. Hassan and S. Sato. Interaction nets with nested pattern matching. ENTCS, 203(1):79–92, 2008. Google ScholarGoogle ScholarDigital LibraryDigital Library
  16. J. Hoffmann, K. Aehlig, and M. Hofmann. Multivariate amortized resource analysis. TOPLAS, 34(3):14, 2012. Google ScholarGoogle ScholarDigital LibraryDigital Library
  17. J. Hoffmann and Z. Shao. Automatic static cost analysis for parallel programs. In Proc. 24th ESOP, volume 9032 of LNCS, pages 132–157, 2015. Google ScholarGoogle ScholarDigital LibraryDigital Library
  18. Y. Lafont. Interaction nets. In Proc. 17th POPL, pages 95–108. ACM, 1990. Google ScholarGoogle ScholarDigital LibraryDigital Library
  19. Y. Lafont. Interaction combinators. IC, 137(1):69–101, 1997. Google ScholarGoogle ScholarDigital LibraryDigital Library
  20. U. Dal Lago. Context semantics, linear logic, and computational complexity. TOCL, 10(4), 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  21. U. Dal Lago and B. Petit. Linear dependent types in a call-by-value scenario. Sci. Comput. Program., 84:77–100, 2014. Google ScholarGoogle ScholarDigital LibraryDigital Library
  22. J. Lamping. An algorithm for optimal lambda calculus reduction. In Proc. 7th POPL, pages 16–30. ACM Press, 1990. Google ScholarGoogle ScholarDigital LibraryDigital Library
  23. S. Lippi. Universal hard interaction for clockless computation: Dem Glücklichen schlägt keine Stunde! FI, 91(2):357–394, 2009. Google ScholarGoogle ScholarDigital LibraryDigital Library
  24. The linear logic wiki: Fragments. http://llwiki.ens-lyon.fr/ mediawiki/index.php/Fragment.Google ScholarGoogle Scholar
  25. I. Mackie. Interaction nets for linear logic. TCS, 247(1-2):83–140, 2000. Google ScholarGoogle ScholarDigital LibraryDigital Library
  26. I. Mackie. Efficient lambda-evaluation with interaction nets. In Proc. 15th RTA, volume 3091 of LNCS, pages 155–169, 2004.Google ScholarGoogle Scholar
  27. D. Mazza. Interaction Nets: Semantics and Concurrent Extensions. PhD thesis, 2006.Google ScholarGoogle Scholar
  28. P.-A. Mellies. Functorial boxes in string diagrams. In Proc. 15th CSL, LNCS, pages 1–30, 2006. Google ScholarGoogle ScholarDigital LibraryDigital Library
  29. M. Perrinel. On context semantics and interaction nets. In Proc. Joint 23rd CSL and 29th LICS, page 73. ACM, 2014. Google ScholarGoogle ScholarDigital LibraryDigital Library
  30. J. S. Pinto. Parallel evaluation of interaction nets with mpine. In Proc. 12th RTA, volume 2051 of LNCS, pages 353–356, 2001. Google ScholarGoogle ScholarDigital LibraryDigital Library
  31. M. Sinn, F. Zuleger, and H. Veith. A simple and scalable static analysis for bound analysis and amortized complexity analysis. In Proc. 26th CAV, volume 8559 of LNCS, pages 745–761, 2014. Google ScholarGoogle ScholarDigital LibraryDigital Library
  32. P. Vasconcelos. Space Cost Analysis Using Sized Types. PhD thesis, School of Computer Science, University of St. Andrews, 2008.Google ScholarGoogle Scholar
  33. L. Vaux. λ-calcul différentiel et logique classique: interactions combinatoires. PhD thesis, 2007.Google ScholarGoogle Scholar

Index Terms

  1. The complexity of interaction

    Recommendations

    Comments

    Login options

    Check if you have access through your login credentials or your institution to get full access on this article.

    Sign in

    Full Access

    PDF Format

    View or Download as a PDF file.

    PDF

    eReader

    View online with eReader.

    eReader
    About Cookies On This Site

    We use cookies to ensure that we give you the best experience on our website.

    Learn more

    Got it!