Skip to main content
Springer Nature Link
Log in

Interactive Systems: From Folklore to Mathematics

  • Conference paper
  • First Online:
Relational Methods in Computer Science (RelMiCS 2001)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 2561))

Included in the following conference series:

Abstract

This paper gives a brief introduction to finite interactive systems, an abstract mathematical model of agents’ behavior and their interaction. The paper contains the definition of finite interactive systems, examples, and a few simple results. No examples modeling real interactive systems are included, but there are many pointers suggesting how this can be done.

On leave from Departement of Fundamentals of Computer Science, University of Bucharest

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

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.

Similar content being viewed by others

References

  1. A. Arnold. Finite transition systems. Prentice-Hall, 1994.

    Google Scholar 

  2. Borchert, B. http://math.uni-heidelberg.de/logic/bb/2dpapers.html

  3. M. Broy, G. Ciobanu, R. Grosu, and G. Stefanescu. Finite interactive systems: A unified model for agents’ behaviour and their interaction. Draft, December, 2001.

    Google Scholar 

  4. M. Broy and G. Stefanescu. The algebra of stream processing functions. Theorertical Computer Science, 258:95–125, 2001.

    MathSciNet  Google Scholar 

  5. R. Bruni. Tile Logic for Synchronized Rewriting of Concurrent Systems. PhD thesis, Dipartimento di Informatica, Universita di Pisa, 1999. Report TD-1/99.

    Google Scholar 

  6. R. Bruni and U. Montanari. Zero-safe nets, or transition synchronization made simple. Electronic Notes in Theoretical Computer Science, vol. 7(20 pages), 1997.

    Google Scholar 

  7. L. Cardeli and A. Gordon. Anytime, anywhere: modal logics for mobile ambients. In: POPL-2000, Symposium on Principles of Programming Languages, Boston, 2000. ACM Press, 2000.

    Google Scholar 

  8. J.H. Conway. Regular Algebra and Finite Machines. Chapman and Hall, 1971.

    Google Scholar 

  9. V. Garg and M.T. Ragunath. Concurrent regular expressions and their relationship to Petri nets. Theoretical Computer Science, 96:285–304, 1992.

    Article  MATH  MathSciNet  Google Scholar 

  10. D. Giammarresi and A. Restivo. Two-dimensional languages. In G. Rozenberg and A. Salomaa, editors, Handbook of formal languages. Vol. 3: Beyond words, pages 215–265. Springer-Verlag, 1997.

    Google Scholar 

  11. R. Grosu, D. Lucanu, and G. Stefanescu. Mixed relations as enriched semiringal categories. Journal of Universal Computer Science, 6(1):112–129, 2000.

    MATH  MathSciNet  Google Scholar 

  12. R. Grosu, G. Stefanescu, and M. Broy. Visual formalism revised. In Proceeding of the CSD’98 (International Conference on Application of Concurrency to System Design, March 23–26, 1998, Fukushima, Japan), pages 41–51. IEEE Computer Society Press, 1998.

    Google Scholar 

  13. K. Inoue and I. Takanami. A survey of two-dimensional automata theory. Information Sciences, 55:99–121, 1991.

    Article  MATH  MathSciNet  Google Scholar 

  14. S.C. Kleene. Representation of events in nerve nets and finite automata. In: C.E. Shannon and J. McCarthy, eds.,Automata Studies, Annals of Mathematical Studies, vol. 34, 3–41. Princeton University Press, 1956.

    Google Scholar 

  15. D. Kozen. A completeness theorem for Kleene algebras and the algebra of regular events. Information and Computation110:366–390, 1994.

    Article  MATH  MathSciNet  Google Scholar 

  16. K. Lindgren, C. Moore, and M. Nordahl. Complexity of two-dimensional patterns. Journal of Statistical Physics 91:909–951, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  17. G. Stefanescu. Reaction and control I. Mixing additive and multiplicative network algebras. Logic Journal of the IGPL, 6(2):349–368, 1998.

    Article  MATH  MathSciNet  Google Scholar 

  18. G. Stefanescu. Network algebra. Springer-Verlag, 2000.

    Google Scholar 

  19. G. Stefanescu. Kleene algebras of two dimensional words: A model for interactive systems. Dagstuhl Seminar on “Applications of Kleene algebras”, Seminar 01081, 19–23 February, 2001.

    Google Scholar 

  20. G. Stefanescu. Algebra of networks: Modeling simple networks, as well as complex interactive systems. In: H. Schwichtenberg and R. Steibrügen, eds., Proof and System Reliability, 49–78. Kluwer Academic Publishers, 2002.

    Google Scholar 

  21. W. Zielonka. Notes on finite asynchronous automata. Theoretical Informatics and Applications, 21:99–135, 1987.

    MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, National University of Singapore, Singapore

    Gheorghe ŞtefĂnescu

Authors
  1. Gheorghe ŞtefĂnescu
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Tilburg University, P.O. Box 90153, 5000, LE Tilburg, The Netherlands

    Harrie C. M. de Swart

Rights and permissions

Reprints and permissions

Copyright information

© 2002 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

ŞtefĂnescu, G. (2002). Interactive Systems: From Folklore to Mathematics. In: de Swart, H.C.M. (eds) Relational Methods in Computer Science. RelMiCS 2001. Lecture Notes in Computer Science, vol 2561. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36280-0_14

Download citation

  • DOI: https://doi.org/10.1007/3-540-36280-0_14

  • Published:

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-00315-1

  • Online ISBN: 978-3-540-36280-7

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics