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International Conference on Relational and Algebraic Methods in Computer Science

RAMICS 2014: Relational and Algebraic Methods in Computer Science pp 19–36Cite as

Endowing Concurrent Kleene Algebra with Communication Actions

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8428)

Abstract

Communication is integral to the understanding of agent interactions in concurrent systems. In this paper,we propose a mathematical framework for communication and concurrency called Communicating Concurrent Kleene Algebra (C2KA). C2KAextends concurrent Kleene algebra with the notion of communication actions. This extension captures both the influence of external stimuli on agent behaviour aswell as the communication and concurrency of communicating agents.

Keywords

  • concurrency
  • communication
  • concurrent Kleene algebra
  • semimodules
  • specification
  • algebraic approaches to concurrency

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  • DOI: 10.1007/978-3-319-06251-8_2
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References

  1. Bergstra, J., Klop, J.: Process algebra for synchronous communication. Information and Control 60(1-3), 109–137 (1984)

    CrossRef  MATH  MathSciNet  Google Scholar 

  2. Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982)

    CrossRef  Google Scholar 

  3. Clavel, M., Durán, F., Eker, S., Lincoln, P., Martí-Oliet, N., Meseguer, J., Talcott, C.: The Maude 2.0 System. In: Nieuwenhuis, R. (ed.) RTA 2003. LNCS, vol. 2706, pp. 76–87. Springer, Heidelberg (2003)

    CrossRef  Google Scholar 

  4. Cleaveland, R., Smolka, S.: Strategic directions in concurrency research. ACM Computing Surveys 28(4), 607–625 (1996)

    CrossRef  Google Scholar 

  5. Emerson, E., Halpern, J.: “sometimes” and “not never” revisited: On branching versus linear time temporal logic. Journal of the ACM 33(1), 151–178 (1986)

    CrossRef  MATH  MathSciNet  Google Scholar 

  6. Hebisch, U., Weinert, H.: Semirings: Algebraic Theory and Applications in Computer Science. Series in Algebra, vol. 5. World Scientific (1993)

    Google Scholar 

  7. Hoare, C.: Communicating sequential processes. Communications of the ACM 21(8), 666–677 (1978)

    CrossRef  MATH  MathSciNet  Google Scholar 

  8. Hoare, C.: Communicating Sequential Processes. Prentice-Hall (1985)

    Google Scholar 

  9. Hoare, C., Möller, B., Struth, G., Wehrman, I.: Concurrent Kleene algebra. In: Bravetti, M., Zavattaro, G. (eds.) CONCUR 2009. LNCS, vol. 5710, pp. 399–414. Springer, Heidelberg (2009)

    CrossRef  Google Scholar 

  10. Hoare, C., Möller, B., Struth, G., Wehrman, I.: Foundations of concurrent Kleene algebra. In: Berghammer, R., Jaoua, A.M., Möller, B. (eds.) RelMiCS/AKA 2009. LNCS, vol. 5827, pp. 166–186. Springer, Heidelberg (2009)

    Google Scholar 

  11. Hoare, C., Möller, B., Struth, G., Wehrman, I.: Concurrent Kleene algebra and its foundations. Tech. Rep. CS-10-04, University of Sheffield, Department of Computer Science, Sheffield, UK (August 2010), http://www.dcs.shef.ac.uk/~georg/ka/

  12. Hoare, C., Möller, B., Struth, G., Wehrman, I.: Concurrent Kleene algebra and its foundations. Journal of Logic and Algebraic Programming 80(6), 266–296 (2011)

    CrossRef  MATH  MathSciNet  Google Scholar 

  13. Hoare, C., Wickerson, J.: Unifying models of data flow. In: Broy, M., Leuxner, C., Hoare, C. (eds.) Proceedings of the 2010 Marktoberdorf Summer School on Software and Systems Safety, pp. 211–230. IOS Press (August 2011)

    Google Scholar 

  14. Holcombe, W.: Algebraic Automata Theory. Cambridge Studies in Advanced Mathematics. Cambridge University Press (2004)

    Google Scholar 

  15. Jaskolka, J., Khedri, R., Zhang, Q.: On the necessary conditions for covert channel existence: A state-of-the-art survey. Procedia Computer Science 10, 458–465 (2012); Proceedings of the 3rd International Conference on Ambient Systems, Networks and Technologies, ANT 2012 (2012)

    Google Scholar 

  16. Jaskolka, J., Khedri, R., Zhang, Q.: Foundations of communicating concurrent Kleene algebra. Tech. Rep. CAS-13-07-RK, McMaster University, Hamilton, Ontario, Canada (November 2013), http://www.cas.mcmaster.ca/cas/0template1.php?601

  17. Keller, R.: Formal verification of parallel programs. Communications of the ACM 19(7), 371–384 (1976)

    CrossRef  MATH  Google Scholar 

  18. Kilp, M., Knauer, U., Mikhalev, A.: Monoids, Acts And Categories With Applications to Wreath Products and Graphs: A Handbook for Students and Researchers. De Gruyter Expositions in Mathematics Series, vol. 29. Walter de Gruyter (2000)

    Google Scholar 

  19. Kozen, D.: Automata and Computability. Undergraduate Texts in Computer Science. Springer (1997)

    Google Scholar 

  20. Linton, S., Pfeiffer, G., Robertson, E., Ruškuc, N.: Computing transformation semigroups. Journal of Symbolic Computation 33(2), 145–162 (2002)

    CrossRef  MATH  MathSciNet  Google Scholar 

  21. Mazurkiewicz, A.: Trace theory. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 278–324. Springer, Heidelberg (1987)

    Google Scholar 

  22. Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)

    CrossRef  Google Scholar 

  23. Milner, R.: Communication and Concurrency. Prentice-Hall International Series in Computer Science. Prentice Hall (1989)

    Google Scholar 

  24. Milner, R., Parrow, J., Walker, D.: A calculus of mobile processes part I. Information and Computation 100(1), 1–40 (1992)

    CrossRef  MATH  MathSciNet  Google Scholar 

  25. Petri, C.: Kommunikation mit Automaten. Ph.D. thesis, Institut für instrumentelle Mathematik, Bonn, Germany (1962), English translation available as: Communication with Automata, Technical Report RADC-TR-65-377, vol. 1, supplement 1, Applied Data Research, Princeton, NJ (1966)

    Google Scholar 

  26. Pnueli, A.: The temporal logic of programs. In: Proceedings of the 18th Annual Symposium on Foundations of Computer Science, pp. 46–57 (1977)

    Google Scholar 

  27. Pratt, V.: Modeling concurrency with partial orders. International Journal of Parallel Programming 15(1), 33–71 (1986)

    CrossRef  MATH  MathSciNet  Google Scholar 

  28. Shields, M.: Implicit system specification and the interface equation. The Computer Journal 32(5), 399–412 (1989)

    CrossRef  MathSciNet  Google Scholar 

  29. Steinberg, B.: A theory of transformation monoids: Combinatorics and representation theory. The Electronic Journal of Combinatorics 17(1) (2010)

    Google Scholar 

  30. Watson, J.: Behaviorism. University of Chicago Press (1930)

    Google Scholar 

  31. Winskel, G.: Event structures. In: Brauer, W., Reisig, W., Rozenberg, G. (eds.) APN 1986. LNCS, vol. 255, pp. 325–392. Springer, Heidelberg (1987)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computing and Software, Faculty of Engineering, McMaster University, Hamilton, Ontario, Canada

    Jason Jaskolka, Ridha Khedri & Qinglei Zhang

Authors
  1. Jason Jaskolka
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  2. Ridha Khedri
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  3. Qinglei Zhang
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Editor information

Editors and Affiliations

  1. NICTA and UNSW, Anzac Parade 223, 2033, Kensington, NSW, Australia

    Peter Höfner

  2. School of Computational Sciences, Chapman University, One University Drive, 92866, Orange, CA, USA

    Peter Jipsen

  3. Department of Computing and Software, McMaster University, 1280 Main Street West, L8S 4K1, Hamilton, ON, Canada

    Wolfram Kahl

  4. Department of Computer Science, University of Augsburg, Universitätsstraße 6a, 86159, Augsburg, Germany

    Martin Eric Müller

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Jaskolka, J., Khedri, R., Zhang, Q. (2014). Endowing Concurrent Kleene Algebra with Communication Actions. In: Höfner, P., Jipsen, P., Kahl, W., Müller, M.E. (eds) Relational and Algebraic Methods in Computer Science. RAMICS 2014. Lecture Notes in Computer Science, vol 8428. Springer, Cham. https://doi.org/10.1007/978-3-319-06251-8_2

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  • DOI: https://doi.org/10.1007/978-3-319-06251-8_2

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-06250-1

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