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Parsimonious Types and Non-uniform Computation

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Automata, Languages, and Programming (ICALP 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9135))

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Abstract

We consider a non-uniform affine lambda-calculus, called parsimonious, and endow its terms with two type disciplines: simply-typed and with linear polymorphism. We show that the terms of string type into Boolean type characterize the class L/poly in the first case, and P/poly in the second. Moreover, we relate this characterization to that given by the second author in terms of Boolean proof nets, highlighting continuous affine approximations as the bridge between the two approaches to non-uniform computation.

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References

  1. Abramsky, S., Jagadeesan, R., Malacaria, P.: Full abstraction for PCF. Inf. Comput. 163(2), 409–470 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  2. Baillot, P., Terui, K.: Light types for polynomial time computation in lambda calculus. Inf. Comput. 207(1), 41–62 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  3. Bellantoni, S., Cook, S.A.: A new recursion-theoretic characterization of the polytime functions. Computational Complexity 2, 97–110 (1992)

    Article  MATH  MathSciNet  Google Scholar 

  4. Ehrhard, T., Regnier, L.: Differential interaction nets. Electr. Notes Theor. Comput. Sci. 123, 35–74 (2005)

    Article  MathSciNet  Google Scholar 

  5. Ehrhard, T., Regnier, L.: Uniformity and the taylor expansion of ordinary lambda-terms. Theor. Comput. Sci. 403(2–3), 347–372 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Gaboardi, M., Péchoux, R.: Upper bounds on stream I/O using semantic interpretations. In: Grädel, E., Kahle, R. (eds.) CSL 2009. LNCS, vol. 5771, pp. 271–286. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  7. Ghica, D.R.: Geometry of synthesis: a structured approach to VLSI design. In: Proceedings of POPL, pp. 363–375 (2007)

    Google Scholar 

  8. Girard, J.Y.: Geometry of interaction I: Interpretation of system F. Proccedings of Logic Colloquium 1988, 221–260 (1989)

    MathSciNet  Google Scholar 

  9. Girard, J.Y.: Light linear logic. Inf. Comput. 143(2), 175–204 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  10. Kfoury, A.J.: A linearization of the lambda-calculus and consequences. J. Log. Comput. 10(3), 411–436 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  11. Leivant, D., Marion, J.Y.: Lambda calculus characterizations of poly-time. Fundam. Inform. 19(1/2) (1993)

    Google Scholar 

  12. Mazza, D.: An infinitary affine lambda-calculus isomorphic to the full lambda-calculus. In: Proceedings of LICS, pp. 471–480 (2012)

    Google Scholar 

  13. Mazza, D.: Non-uniform polytime computation in the infinitary affine lambda-calculus. In: Esparza, J., Fraigniaud, P., Husfeldt, T., Koutsoupias, E. (eds.) ICALP 2014, Part II. LNCS, vol. 8573, pp. 305–317. Springer, Heidelberg (2014)

    Google Scholar 

  14. Mazza, D.: Simple parsimonious types and logarithmic space (2015), available on the author’s web page

    Google Scholar 

  15. Melliès, P.A.: Asynchronous games 2: The true concurrency of innocence. Theor. Comput. Sci. 358(2–3), 200–228 (2006)

    Article  MATH  Google Scholar 

  16. Melliès, P.-A., Tabareau, N., Tasson, C.: An explicit formula for the free exponential modality of linear logic. In: Albers, S., Marchetti-Spaccamela, A., Matias, Y., Nikoletseas, S., Thomas, W. (eds.) ICALP 2009, Part II. LNCS, vol. 5556, pp. 247–260. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  17. Ramyaa, R., Leivant, D.: Ramified corecurrence and logspace. Electr. Notes Theor. Comput. Sci. 276, 247–261 (2011)

    Article  MathSciNet  Google Scholar 

  18. Saurin, A.: Typing streams in the \(\Lambda \mu \)-calculus. ACM Trans. Comput. Log. 11(4) (2010)

    Google Scholar 

  19. Terui, K.: Proof nets and boolean circuits. In: Proceedings of LICS, pp. 182–191 (2004)

    Google Scholar 

  20. Vollmer, H.: Introduction to circuit complexity - a uniform approach. Texts in theoretical computer science. Springer (1999)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CNRS, UMR 7030, LIPN, Université Paris 13, Sorbonne Paris Cité, Villetaneuse, France

    Damiano Mazza

  2. RIMS, Kyoto University, Kyoto, Japan

    Kazushige Terui

Authors
  1. Damiano Mazza
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  2. Kazushige Terui
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Corresponding author

Correspondence to Damiano Mazza .

Editor information

Editors and Affiliations

  1. Reykjavik University, Reykjavik, Iceland

    Magnús M. Halldórsson

  2. Kyoto University, Kyoto, Japan

    Kazuo Iwama

  3. The University of Tokyo, Tokyo, Japan

    Naoki Kobayashi

  4. Technische Universiteit Eindhoven, Eindhoven, The Netherlands

    Bettina Speckmann

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Mazza, D., Terui, K. (2015). Parsimonious Types and Non-uniform Computation. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47666-6_28

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  • DOI: https://doi.org/10.1007/978-3-662-47666-6_28

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-662-47665-9

  • Online ISBN: 978-3-662-47666-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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