Location via proxy:   [ UP ]  
[Report a bug]   [Manage cookies]                
Skip to main content
Springer Nature Link
Log in

On the Word Problem for \({\it \Sigma\Pi}\)-Categories, and the Properties of Two-Way Communication

(Extended Abstract)

  • Conference paper
Computer Science Logic (CSL 2009)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5771))

Included in the following conference series:

  • 590 Accesses

Abstract

This paper presents a feasible decision procedure for the equality of parallel arrows in the initial category with finite products and coproducts. The algorithm, in particular, handles the “additive units” and demonstrates that the complications introduced by the presence of these units can be managed in an efficient manner.

This problem is directly related to the problem of determining the equivalence between (finite) processes communicating on a two-way channel.

Research partially supported by the project SOAPDC no. ANR-05-JCJC-0142.

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

Access this chapter

Log in via an institution

Institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. Lambek, J.: Deductive systems and categories. I. Syntactic calculus and residuated categories. Math. Systems Theory 2, 287–318 (1968)

    Article  MathSciNet  MATH  Google Scholar 

  2. Došen, K.: Cut elimination in categories. Trends in Logic—Studia Logica Library, vol. 6. Kluwer Academic Publishers, Dordrecht (1999)

    MATH  Google Scholar 

  3. Cockett, J.R.B., Seely, R.A.G.: Finite sum-product logic. Theory Appl. Categ. 8, 63–99 (2001) (electronic)

    MathSciNet  MATH  Google Scholar 

  4. Hu, H., Joyal, A.: Coherence completions of categories. Theoret. Comput. Sci. 227(1-2), 153–184 (1999), Linear logic, I (Tokyo, 1996)

    Article  MathSciNet  MATH  Google Scholar 

  5. Hughes, D.J.D.: A cannonical graphical syntax for non-empty finite products and sums. Technical report, Stanford University (December 2002), http://boole.stanford.edu/~dominic/papers

  6. Došen, K., Petrić, Z.: Bicartesian coherence revisited. In: Ognjanovic, Z. (ed.) Logic in Computer Science, Zbornik Radova, vol. 12 (2009), arXiv:0711.4961

    Google Scholar 

  7. Hughes, D.J.D., van Glabbeek, R.J.: Proof nets for unit-free multiplicative-additive linear logic (extended abstract). In: LICS, pp. 1–10. IEEE Computer Society, Los Alamitos (2003)

    Google Scholar 

  8. Hu, H.: Contractible coherence spaces and maximal maps. Electr. Notes Theor. Comput. Sci. 20 (1999)

    Google Scholar 

  9. Joyal, A.: Free lattices, communication and money games. In: Logic and scientific methods (Florence, 1995). Synthese Lib., vol. 259, pp. 29–68. Kluwer Acad. Publ, Dordrecht (1997)

    Chapter  Google Scholar 

  10. Santocanale, L.: Free μ-lattices. J. Pure Appl. Algebra 168(2-3), 227–264 (2002), Category theory 1999 (Coimbra)

    Article  MathSciNet  MATH  Google Scholar 

  11. Blass, A.: A game semantics for linear logic. Ann. Pure Appl. Logic 56(1-3), 183–220 (1992)

    Article  MathSciNet  MATH  Google Scholar 

  12. Abramsky, S., Jagadeesan, R.: Games and full completeness for multiplicative linear logic. J. of Symb. Logic 59(2), 543–574 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  13. Cockett, J.R.B., Pastro, C.A.: A language for multiplicative-additive linear logic. Electr. Notes Theor. Comput. Sci. 122, 23–65 (2005)

    Article  MathSciNet  MATH  Google Scholar 

  14. Cockett, J.R.B., Pastro, C.A.: The logic of message passing. Science of Computer Programming 74(8), 498–533 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  15. Mac Lane, S.: Categories for the working mathematician, 2nd edn. Graduate Texts in Mathematics, vol. 5. Springer, New York (1998)

    MATH  Google Scholar 

  16. Joyal, A.: Free bicomplete categories. C. R. Math. Rep. Acad. Sci. Canada 17(5), 219–224 (1995)

    MathSciNet  MATH  Google Scholar 

  17. Joyal, A.: Free bicompletion of enriched categories. C. R. Math. Rep. Acad. Sci. Canada 17(5), 213–218 (1995)

    MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Calgary, Canada

    Robin Cockett

  2. Laboratoire d’Informatique Fondamentale de Marseille, Université Aix-Marseille I, France

    Luigi Santocanale

Authors
  1. Robin Cockett
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Luigi Santocanale
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Mathematische Grundlagen der Informatik, RWTH Aachen, 52056, Aachen, Germany

    Erich Grädel

  2. CENTRIA and Departamento de Matemática, Universidade Nova de Lisboa, 2829-516, Caparica, Portugal

    Reinhard Kahle

Rights and permissions

Reprints and permissions

Copyright information

© 2009 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Cockett, R., Santocanale, L. (2009). On the Word Problem for \({\it \Sigma\Pi}\)-Categories, and the Properties of Two-Way Communication . In: Grädel, E., Kahle, R. (eds) Computer Science Logic. CSL 2009. Lecture Notes in Computer Science, vol 5771. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04027-6_16

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-04027-6_16

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-04026-9

  • Online ISBN: 978-3-642-04027-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation