The Power of Priority Channel Systems

  • Christoph Haase
  • Sylvain Schmitz
  • Philippe Schnoebelen
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8052)


We introduce Priority Channel Systems, a new natural class of channel systems where messages carry a numeric priority and where higher-priority messages can supersede lower-priority messages preceding them in the fifo communication buffers. The decidability of safety and inevitability properties is shown via the introduction of a priority embedding, a well-quasi-ordering that has not previously been used in well-structured systems. We then show how Priority Channel Systems can compute Fast-Growing functions and prove that the aforementioned verification problems are F ε0-complete.


Channel System Full Version Canonical Factorization Hardy Function Ordinal Term 
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  1. 1.
    Abdulla, P.A., Atig, M.F., Cederberg, J.: Timed lossy channel systems. In: FST&TCS 2012. LIPIcs, vol. 18, pp. 374–386. Leibniz-Zentrum für Informatik (2012)Google Scholar
  2. 2.
    Abdulla, P.A., Čerāns, K., Jonsson, B., Tsay, Y.K.: Algorithmic analysis of programs with well quasi-ordered domains. Inform. and Comput. 160(1-2), 109–127 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  3. 3.
    Abdulla, P.A., Deneux, J., Ouaknine, J., Worrell, J.: Decidability and complexity results for timed automata via channel machines. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds.) ICALP 2005. LNCS, vol. 3580, pp. 1089–1101. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  4. 4.
    Abdulla, P.A., Jonsson, B.: Verifying programs with unreliable channels. Inform. and Comput. 127(2), 91–101 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  5. 5.
    Bansal, K., Koskinen, E., Wies, T., Zufferey, D.: Structural counter abstraction. In: Piterman, N., Smolka, S.A. (eds.) TACAS 2013. LNCS, vol. 7795, pp. 62–77. Springer, Heidelberg (2013)Google Scholar
  6. 6.
    Boigelot, B., Godefroid, P.: Symbolic verification of communication protocols with infinite state spaces using QDDs. Form. Methods in Syst. Des. 14(3), 237–255 (1999)CrossRefGoogle Scholar
  7. 7.
    Bouajjani, A., Habermehl, P.: Symbolic reachability analysis of FIFO-channel systems with nonregular sets of configurations. Theor. Comput. Sci. 221(1-2), 211–250 (1999)MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    Bouyer, P., Markey, N., Ouaknine, J., Schnoebelen, P., Worrell, J.: On termination and invariance for faulty channel machines. Form. Asp. Comput. 24(4-6), 595–607 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Cécé, G., Finkel, A.: Verification of programs with half-duplex communication. Inform. and Comput. 202(2), 166–190 (2005)MathSciNetzbMATHCrossRefGoogle Scholar
  10. 10.
    Cécé, G., Finkel, A., Purushothaman Iyer, S.: Unreliable channels are easier to verify than perfect channels. Inform. and Comput. 124(1), 20–31 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  11. 11.
    Chambart, P., Schnoebelen, P.: The ordinal recursive complexity of lossy channel systems. In: LICS 2008, pp. 205–216. IEEE Press (2008)Google Scholar
  12. 12.
    Delzanno, G., Sangnier, A., Zavattaro, G.: Parameterized verification of ad hoc networks. In: Gastin, P., Laroussinie, F. (eds.) CONCUR 2010. LNCS, vol. 6269, pp. 313–327. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  13. 13.
    Fairtlough, M., Wainer, S.S.: Hierarchies of provably recursive functions. In: Handbook of Proof Theory, ch. III, pp. 149–207. Elsevier (1998)Google Scholar
  14. 14.
    Finkel, A., Schnoebelen, P.: Well-structured transition systems everywhere! Theor. Comput. Sci. 256(1-2), 63–92 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  15. 15.
    Genest, B., Muscholl, A., Serre, O., Zeitoun, M.: Tree pattern rewriting systems. In: Cha, S(S.), Choi, J.-Y., Kim, M., Lee, I., Viswanathan, M. (eds.) ATVA 2008. LNCS, vol. 5311, pp. 332–346. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  16. 16.
    Gupta, A.: A constructive proof that trees are well-quasi-ordered under minors. In: Nerode, A., Taitslin, M.A. (eds.) LFCS 1992. LNCS, vol. 620, pp. 174–185. Springer, Heidelberg (1992)CrossRefGoogle Scholar
  17. 17.
    Haddad, S., Schmitz, S., Schnoebelen, P.: The ordinal-recursive complexity of timed-arc Petri nets, data nets, and other enriched nets. In: LICS 2012, pp. 355–364. IEEE Press (2012)Google Scholar
  18. 18.
    Kurucz, A.: Combining modal logics. In: Handbook of Modal Logics, ch. 15, pp. 869–926. Elsevier (2006)Google Scholar
  19. 19.
    Lasota, S., Walukiewicz, I.: Alternating timed automata. ACM Trans. Comput. Logic 9(2) (2008)Google Scholar
  20. 20.
    Löb, M., Wainer, S.: Hierarchies of number theoretic functions. I. Arch. Math. Logic 13, 39–51 (1970)zbMATHCrossRefGoogle Scholar
  21. 21.
    Ossona de Mendez, P., Nešetřil, J.: Sparsity, ch. 6. Bounded height trees and tree-depth, pp. 115–144. Springer (2012)Google Scholar
  22. 22.
    Meyer, R.: On boundedness in depth in the π-calculus. In: Ausiello, G., Karhumäki, J., Mauri, G., Ong, L. (eds.) IFIP TCS 2008. IFIP, vol. 273, pp. 477–489. Springer, Boston (2008)Google Scholar
  23. 23.
    Ouaknine, J., Worrell, J.: On the decidability and complexity of Metric Temporal Logic over finite words. Logic. Meth. Logic. Meth. in Comput. Sci. 3(1), 1–27 (2007)MathSciNetGoogle Scholar
  24. 24.
    Schmitz, S., Schnoebelen, P.: Multiply-recursive upper bounds with Higman’s lemma. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011, Part II. LNCS, vol. 6756, pp. 441–452. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  25. 25.
    Schmitz, S., Schnoebelen, P.: Algorithmic aspects of WQO theory. Lecture notes (2012),
  26. 26.
    Schnoebelen, P.: Lossy counter machines decidability cheat sheet. In: Kučera, A., Potapov, I. (eds.) RP 2010. LNCS, vol. 6227, pp. 51–75. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  27. 27.
    Schnoebelen, P.: Revisiting Ackermann-hardness for lossy counter machines and reset Petri nets. In: Hliněný, P., Kučera, A. (eds.) MFCS 2010. LNCS, vol. 6281, pp. 616–628. Springer, Heidelberg (2010)CrossRefGoogle Scholar
  28. 28.
    Schütte, K., Simpson, S.G.: Ein in der reinen Zahlentheorie unbeweisbarer Satz über endliche Folgen von natürlichen Zahlen. Arch. Math. Logic 25(1), 75–89 (1985)zbMATHCrossRefGoogle Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Christoph Haase
    • 1
  • Sylvain Schmitz
    • 1
  • Philippe Schnoebelen
    • 1
  1. 1.LSVENS Cachan & CNRSFrance

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