Towards automata for branching time and partial order

  • Michaela Huhn
  • Peter Niebert
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 1119)


In this work we develop an automata framework for partial order structures with branching, for which we use trace systems. The aim is to investigate the prospects of decidable partial order logics of branching time, derivable from an automata framework.

On the one hand we define automata for trace systems directly, which combine asynchronous automata for linear time with tree automata. On the other hand we develop a branching generalisation of Mazurkiewicz trace theory, which links branching concurrent behaviour with tree automata directly: the idea is to generalise interleaving sequences for partially ordered runs to interleaving trees for trace systems. This development can also be used for partial order reduction methods in model checking for branching time.

The latter approach also exposes a problem for the specification of branching time and concurrent behaviour: the distinction between nondeterministic choice and parallelism cannot be maintained completely in the presence of confusion, a notion known from Petri net theory. We discuss several possible ways of coping with this problem.

Also on the automata side there are a few surprises. In particular the emptiness problem is decidable as desired, but turns out to be co-NP-complete.


Partial Order Model Check Tree Automaton Trace System Linear Time Temporal Logic 
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.


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  1. [BVW94]
    Orna Bernholtz, Moshe Y. Vardi, and Pierre Wolper. An automata-theoretic approach to branching-time model checking. In CAV 94, LNCS 818, pp 142–153, 1994.Google Scholar
  2. [DE95]
    Jörg Desel and Javier Esparza. Free choice Petri nets. Cambridge tracts in theoretical computer science 40, Cambridge University Press, 1995Google Scholar
  3. [GJ79]
    M.R. Garey and D.S. Johnson. Computers and Intractability. Freeman, NY 1979.Google Scholar
  4. [GLT79]
    H.J. Genrich and K. Lautenbach and P.S. Thiagarajan. Elements of general net theory. In Net Theory and Applications, LNCS 84, pages 21–159, 1979.Google Scholar
  5. [GKPP95]
    R. Gerth, R. Kuiper, D. Peled, and W. Penczek. A partial order approach to branching time logic model checking. In Israeli Symp. on Theoretical Comp. Sci., 1995.Google Scholar
  6. [HN96]
    Michaela Huhn and Peter Niebert. Towards automata for branching time and partial order. Report HIB 16/96. Institute for Informatics, Univ. Hildesheim. 1996.Google Scholar
  7. [KP95]
    Ruurd Kuiper and Wojciech Penczek. Traces and Logic. In V. Diekert and G. Rozenberg (eds.): The Book of Traces, World Scientific, Singapore, 1995, 307–390Google Scholar
  8. [Ma88]
    Antoni Mazurkiewicz. Basic notions of trace theory. LNCS 354, pp 285–363, 1988Google Scholar
  9. [MT90]
    Madhavan Mukund and P. S. Thiagarajan. An axiomatisation of well branching prime event structures. Internal Report TCS-90-2, Inst. of Mathematical Sciences, SPIC Science Foundation, Madras 600 113, India, September 1990.Google Scholar
  10. [NP95]
    Peter Niebert and Wojciech Penczek. On the connection of partial order logics and partial order reduction methods. Report 95-15, TU Eindhoven, CS Dept, 1995.Google Scholar
  11. [NW95]
    M. Nielsen and G. Winskel. Models for concurrency. in S. Abramsky, D.M Gabbay, T.S.E. Maibaum (eds.): Handbook of Logic in Computer Science, Volume 4 Semantic Modelling, pages 1–148, Oxford University Press 1995.Google Scholar
  12. [Pel93]
    Doron Peled. All from one, one for all: on model checking using representatives. In Computer Aided Verification, LNCS 697, 1993.Google Scholar
  13. [Pen92]
    Wojciech Penczek. On undecidability of propositional temporal logics on trace systems. Information Processing Letters 43, 147–153, 1992Google Scholar
  14. [RT91]
    B. Rozoy and P.S. Thiagarajan. Event structures and trace monoids, Theoretical Computer Science 91, 285–313, 1991.Google Scholar
  15. [Sta89]
    E.W. Stark. Concurrent transition systems. In Theoretical Computer Science 64: 221–269,1989.Google Scholar
  16. [Thi94]
    P.S. Thiagarajan. A trace based extension of Linear Time Temporal Logic. In Proc. of the 9th annual IEEE Symposium on Logic in Computer Science (LICS), 1994.Google Scholar
  17. [Thi95]
    P.S. Thiagarajan. A trace consistent subset of PTL. In CONCUR '95, LNCS 962, 1995.Google Scholar
  18. [Tho90]
    Wolfgang Thomas. Automata on infinite objects. In J. v. Leeuwen (ed.), Handbook of Theoretical Computer Science, vol. B, ch. 4, pages 133–191. Elsevier, 1990.Google Scholar
  19. [VW86]
    Moshe Y. Vardi and Pierre Wolper. An automata-theoretic approach to automatic program verification. In 1st IEEE Symp. Logic in Comp. Sci. (LICS), p. 332–344, 1986.Google Scholar
  20. [Win87]
    Glynn Winskel. Event structures. In Advances in Petri Nets, LNCS 255, 1987.Google Scholar
  21. [Zie89]
    Wieslaw Zielonka. Safe executions of recognisable trace languages by asynchronous automata. In Logic at Botik, LNCS 363, pages 278–289, 1989.Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1996

Authors and Affiliations

  • Michaela Huhn
    • 1
  • Peter Niebert
    • 1
  1. 1.Institut für InformatikUniversität HildesheimGermany

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