Skip to main content
SpringerLink
Log in

Logic Programming and Logarithmic Space

  • Conference paper
Programming Languages and Systems (APLAS 2014)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 8858))

Included in the following conference series:

Abstract

We present an algebraic view on logic programming, related to proof theory and more specifically linear logic and geometry of interaction. Within this construction, a characterization of logspace (deterministic and non-deterministic) computation is given via a syntactic restriction, using an encoding of words that derives from proof theory.

We show that the acceptance of a word by an observation (the counterpart of a program in the encoding) can be decided within logarithmic space, by reducing this problem to the acyclicity of a graph. We show moreover that observations are as expressive as two-ways multihead finite automata, a kind of pointer machine that is a standard model of logarithmic space computation.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

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

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Asperti, A., Danos, V., Laneve, C., Regnier, L.: Paths in the lambda-calculus. In: LICS, pp. 426–436. IEEE Computer Society (1994)

    Google Scholar 

  2. Aubert, C., Bagnol, M.: Unification and logarithmic space. In: Dowek, G. (ed.) RTA-TLCA 2014. LNCS, vol. 8560, pp. 77–92. Springer, Heidelberg (2014)

    Chapter  Google Scholar 

  3. Aubert, C., Seiller, T.: Characterizing co-nl by a group action. Arxiv preprint abs/1209.3422 (2012)

    Google Scholar 

  4. Baader, F., Snyder, W.: Unification theory. In: Robinson, J.A., Voronkov, A. (eds.) Handbook of Automated Reasoning, pp. 445–532. Elsevier and MIT Press (2001)

    Google Scholar 

  5. Baillot, P., Mazza, D.: Linear logic by levels and bounded time complexity. Theoret. Comput. Sci. 411(2), 470–503 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  6. Baillot, P., Pedicini, M.: Elementary complexity and geometry of interaction. Fund. Inform. 45(1-2), 1–31 (2001)

    MathSciNet  MATH  Google Scholar 

  7. Bellia, M., Occhiuto, M.E.: N-axioms parallel unification. Fund. Inform. 55(2), 115–128 (2003)

    MathSciNet  MATH  Google Scholar 

  8. Ben-Amram, A.M.: What is a “pointer machine”? Science of Computer Programming 26, 88–95 (1995)

    Google Scholar 

  9. Calimeri, F., Cozza, S., Ianni, G., Leone, N.: Computable functions in ASP: Theory and implementation. In: Garcia de la Banda, M., Pontelli, E. (eds.) ICLP 2008. LNCS, vol. 5366, pp. 407–424. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  10. Dal Lago, U., Hofmann, M.: Bounded linear logic, revisited. Log. Meth. Comput. Sci. 6(4) (2010)

    Google Scholar 

  11. Dantsin, E., Eiter, T., Gottlob, G., Voronkov, A.: Complexity and expressive power of logic programming. ACM Comput. Surv. 33(3), 374–425 (2001)

    Article  Google Scholar 

  12. Dwork, C., Kanellakis, P.C., Mitchell, J.C.: On the sequential nature of unification. J. Log. Program. 1(1), 35–50 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  13. Dwork, C., Kanellakis, P.C., Stockmeyer, L.J.: Parallel algorithms for term matching. SIAM J. Comput. 17(4), 711–731 (1988)

    Article  MathSciNet  MATH  Google Scholar 

  14. Gaboardi, M., Marion, J.Y., Ronchi Della Rocca, S.: An implicit characterization of pspace. ACM Trans. Comput. Log. 13(2), 18:1–18:36 (2012)

    Google Scholar 

  15. Girard, J.Y.: Linear logic. Theoret. Comput. Sci. 50(1), 1–101 (1987)

    Article  MathSciNet  MATH  Google Scholar 

  16. Girard, J.Y.: Geometry of interaction 1: Interpretation of system F. Studies in Logic and the Foundations of Mathematics 127, 221–260 (1989)

    Article  MathSciNet  Google Scholar 

  17. Girard, J.Y.: Towards a geometry of interaction. In: Gray, J.W., Ščedrov, A. (eds.) Proceedings of the AMS-IMS-SIAM Joint Summer Research Conference held, June 14-20. Categories in Computer Science and Logic, vol. 92, pp. 69–108. AMS (1989)

    Google Scholar 

  18. Girard, J.Y.: Geometry of interaction III: Accommodating the additives. In: Girard, J.Y., Lafont, Y., Regnier, L. (eds.) Advances in Linear Logic. London Math. Soc. Lecture Note Ser., vol. 222, pp. 329–389. CUP (1995)

    Google Scholar 

  19. Girard, J.Y.: Light linear logic. In: Leivant, D. (ed.) LCC 1994. LNCS, vol. 960, pp. 145–176. Springer, Heidelberg (1995)

    Chapter  Google Scholar 

  20. Girard, J.Y.: Normativity in logic. In: Dybjer, P., Lindstrm, S., Palmgren, E., Sundholm, G. (eds.) Epistemology versus Ontology. Logic, Epistemology, and the Unity of Science, vol. 27, pp. 243–263. Springer (2012)

    Google Scholar 

  21. Girard, J.Y.: Three lightings of logic. In: Ronchi Della Rocca, S. (ed.) CSL. LIPIcs, vol. 23, pp. 11–23. Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2013)

    Google Scholar 

  22. Hillebrand, G.G., Kanellakis, P.C., Mairson, H.G., Vardi, M.Y.: Undecidable boundedness problems for datalog programs. J. Log. Program. 25(2), 163–190 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  23. Holzer, M., Kutrib, M., Malcher, A.: Multi-head finite automata: Characterizations, concepts and open problems. In: Neary, T., Woods, D., Seda, A.K., Murphy, N. (eds.) CSP. EPTCS, vol. 1, pp. 93–107 (2008)

    Google Scholar 

  24. Jones, N.D.: Space-bounded reducibility among combinatorial problems. J. Comput. Syst. Sci. 11(1), 68–85 (1975)

    Article  MATH  Google Scholar 

  25. Laurent, O.: A token machine for full geometry of interaction (extended abstract). In: Abramsky, S. (ed.) TLCA 2001. LNCS, vol. 2044, pp. 283–297. Springer, Heidelberg (2001)

    Chapter  Google Scholar 

  26. Lierler, Y., Lifschitz, V.: One more decidable class of finitely ground programs. In: Hill, P.M., Warren, D.S. (eds.) ICLP 2009. LNCS, vol. 5649, pp. 489–493. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  27. Ohkubo, M., Yasuura, H., Yajima, S.: On parallel computation time of unification for restricted terms. Tech. rep., Kyoto University (1987)

    Google Scholar 

  28. Pighizzini, G.: Two-way finite automata: Old and recent results. Fund. Inform. 126(2-3), 225–246 (2013)

    MathSciNet  MATH  Google Scholar 

  29. Robinson, J.A.: A machine-oriented logic based on the resolution principle. J. ACM 12(1), 23–41 (1965)

    Article  MATH  Google Scholar 

  30. Savage, J.E.: Models of computation - exploring the power of computing. Addison-Wesley (1998)

    Google Scholar 

  31. Schöpp, U.: Stratified bounded affine logic for logarithmic space. In: LICS, pp. 411–420. IEEE Computer Society (2007)

    Google Scholar 

  32. Seiller, T.: Interaction graphs: Multiplicatives. Ann. Pure Appl. Logic 163, 1808–1837 (2012)

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. CNRS, Centrale Marseille, I2M UMR 7373, Aix Marseille Université, 13453, Marseille, France

    Clément Aubert, Marc Bagnol & Paolo Pistone

  2. I.H.É.S., Le Bois-Marie, 35, Route de Chartres, 91440, Bures-sur-Yvette, France

    Thomas Seiller

Authors
  1. Clément Aubert
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Marc Bagnol
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Paolo Pistone
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Thomas Seiller
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Graduate School of Mathematics, Nagoya University, 464-8602, Chikusa-ku, Nagoya, Japan

    Jacques Garrigue

Rights and permissions

Reprints and permissions

Copyright information

© 2014 Springer International Publishing Switzerland

About this paper

Cite this paper

Aubert, C., Bagnol, M., Pistone, P., Seiller, T. (2014). Logic Programming and Logarithmic Space. In: Garrigue, J. (eds) Programming Languages and Systems. APLAS 2014. Lecture Notes in Computer Science, vol 8858. Springer, Cham. https://doi.org/10.1007/978-3-319-12736-1_3

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-12736-1_3

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-12735-4

  • Online ISBN: 978-3-319-12736-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation