Advertisement

Towards a Characterisation of Finite-State Message-Passing Systems

  • Madhavan Mukund
  • K. Narayan Kumar
  • Jaikumar Radhakrishnan
  • Milind Sohoni
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1538)

Abstract

We investigate an automata-theoretic model of distributed systems which communicate via message-passing. Each node in the system is a finite-state device. Channels are assumed to be reliable but may deliver messages out of order. Hence, each channel is modelled as a set of counters, one for each type of message. These counters may not be tested for zero

Though each node in the network is finite-state, the overall system is potentially infinite-state because the counters are unbounded. We work in an interleaved setting where the interactions of the system with the environment are described as sequences. The behaviour of a system is described in terms of the language which it accepts—that is, the set of valid interactions with the environment that are permitted by the system

Our aim is to characterise the class of message-passing systems whose behaviour is finite-state. Our main result is that the language accepted by a message-passing system is regular if and only if both the language and its complement are accepted by message-passing systems. We also exhibit an alternative characterisation of regular message-passing languages in terms of deterministic automata

Keywords

Input Alphabet Deterministic Automaton Product Automaton Springer LNCS Asynchronous Automaton 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. AJ93.
    P.A. Abdulla and B. Jonsson: Verifying programs with unreliable channels, in Proc. 8th IEEE Symp. Logic in Computer Science, Montreal, Canada 1993.Google Scholar
  2. GY80.
    A. Ginzburg and M. Yoeli: Vector Addition Systems and Regular Languages, J. Comput. System. Sci. 20 1980 277–284zbMATHCrossRefMathSciNetGoogle Scholar
  3. G78.
    S.A. Greibach: Remarks on Blind and Partially Blind One-Way Multicounter Machines, Theoret. Comput. Sci 7 1978 311–324.zbMATHCrossRefMathSciNetGoogle Scholar
  4. H75.
    M. Hack: Petri Net Languages, C.S.G. Memo 124, Project MAC, MIT 1975.Google Scholar
  5. H91.
    G.J. Holzmann: Design and validation of computer protocols, Prentice Hall 1991.Google Scholar
  6. J86.
    M. Jantzen: Language Theory of Petri Nets, in W. Brauer, W. Reisig, G. Rozenberg (eds.), Petri Nets: Central Models and Their Properties, Advances in Petri Nets, 1986, Vol 1, Springer LNCS 254 1986 397–412.CrossRefGoogle Scholar
  7. KM69.
    R.M. Karp and R.E. Miller: Parallel Program Schemata, J. Comput. System Sci., 3(4) 1969 167–195.MathSciNetGoogle Scholar
  8. LT87.
    N.A. Lynch and M. Tuttle: Hierarchical Correctness Proofs for Distributed Algorithms, Technical Report MIT/LCS/TR-387, Laboratory for Computer Science, MIT 1987.Google Scholar
  9. M78.
    A. Mazurkiewicz: Concurrent Program Schemes and their Interpretations, Report DAIMI-PB-78, Computer Science Department, Aarhus University, Denmark 1978.Google Scholar
  10. MNRS97.
    M. Mukund, K. Narayan Kumar, J. Radhakrishnan and M. Sohoni: Message-Passing Automata and Asynchronous Communication, Report TCS-97-4, SPIC Mathematical Institute, Madras, India 1997.Google Scholar
  11. MNRS98.
    M. Mukund, K. Narayan Kumar, J. Radhakrishnan and M. Sohoni: Robust Asynchronous Protocols are Finite-State, Proc. ICALP 98, Springer LNCS 1998 (to appear).Google Scholar
  12. PS88.
    P. Panangaden and E.W. Stark: Computations, Residuals, and the Power of Indeterminacy, in T. Lepisto and A. Salomaa (eds.), Proc. ICALP’ 88, Springer LNCS 317 1988 439–454.Google Scholar
  13. Pel87.
    E. Pelz: Closure Properties of Deterministic Petri Nets, Proc. STACS 87, Springer LNCS 247, 1987 371–382.CrossRefGoogle Scholar
  14. Pet81.
    J.L. Peterson: Petri net theory and the modelling of systems, Prentice Hall 1981.Google Scholar
  15. VV80.
    R. Valk and G. Vidal-Naquet: Petri Nets and Regular Languages, J. Comput. System. Sci. 20 1980 299–325.MathSciNetGoogle Scholar
  16. V82.
    G. Vidal-Naquet: Deterministic languages for Petri nets, Application and Theory of Petri Nets, Informatik-Fachberichte 52, Springer-Verlag 1982.Google Scholar
  17. Z87.
    W. Zielonka: Notes on Finite Asynchronous Automata, R.A.I.R.O.—Inf. Théor. et Appl., 21 1987 99–135.MathSciNetzbMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1998

Authors and Affiliations

  • Madhavan Mukund
    • 1
  • K. Narayan Kumar
    • 1
  • Jaikumar Radhakrishnan
    • 2
  • Milind Sohoni
    • 3
  1. 1.SPIC Mathematical InstituteMadrasIndia
  2. 2.Computer Science GroupTata Institute of Fundamental ResearchBombayIndia
  3. 3.Department of Computer Science and EngineeringIndian Institute of TechnologyBombayIndia

Personalised recommendations