Formal Aspects of Computing

, Volume 30, Issue 3–4, pp 463–489 | Cite as

Parameterized verification of monotone information systems

  • Raphaël Chane-Yack-Fa
  • Marc FrappierEmail author
  • Amel Mammar
  • Alain Finkel
Original Article


In this paper, we study the information system verification problem as a parameterized verification one. Informations systems are modeled as multi-parameterized systems in a formal language based on the Algebraic State-Transition Diagrams (ASTD) notation. Then, we use the Well Structured Transition Systems (WSTS) theory to solve the coverability problem for an unbounded ASTD state space. Moreover, we define a new framework to prove the effective pred-basis condition of WSTSs, i.e. the computability of a base of predecessors for every states.


Model checking Parameterized verification Process algebra Well-structured transition systems Well-quasi-ordering Coverability Information systems 


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Funding was provided by Natural Sciences and Engineering Research Council of Canada (Grant No. RGPIN-2014-04162).


  1. ACJT96.
    Abdulla PA, Cerans K, Jonsson B, Tsay YK (1996) General decidability theorems for infinite-state systems. In: Logic in computer science. IEEE, pp 313–321Google Scholar
  2. AHH13.
    Abdulla PA, Haziza F, Holík L (2013) All for the price of few. In: Verification, model checking, and abstract interpretation, volume 7737 of LNCS. Springer, pp 476–495Google Scholar
  3. BB87.
    Bolognesi T, Brinksma E (1987) Introduction to the ISO specification language LOTOS. Comput Netw ISDN Syst 14(1): 25–59CrossRefGoogle Scholar
  4. BH05.
    Bingham JD, Hu AJ (2005) Empirically efficient verification for a class of infinite-state systems. In: Tools and algorithms for the construction and analysis of systems, volume 3440 of LNCS. Springer, pp 77–92Google Scholar
  5. BK84.
    Bergstra JA, Klop JW (1984) Process algebra for synchronous communication. Inf Control 60(1): 109–137MathSciNetCrossRefzbMATHGoogle Scholar
  6. BSM99.
    Bernus, P, Schmidt, G, Mertins, K (eds) (1999) Handbook on architectures of information systems. Springer, BerlinGoogle Scholar
  7. CTV06.
    Clarke E, Talupur M, Veith H (2006) Environment abstraction for parameterized verification. In: Verification, model checking, and abstract interpretation, volume 3855 of LNCS. Springer, pp 126–141Google Scholar
  8. CYF17.
    Chane-Yack-Fa R (2017) Verification of parameterized algebraic state transition diagrams. Technical report, Département d’informatique, Faculté des Sciences, Université de Sherbrooke.
  9. DFS98.
    Dufourd C, Finkel A, Schnoebelen P (1998) Reset nets between decidability and undecidability. In: Automata, languages and programming, volume 1443 of LNCS. Springer, pp 103–115Google Scholar
  10. Din92.
    Ding G (1992) Subgraphs and well-quasi-ordering. J Graph Theory 16(5): 489–502MathSciNetCrossRefzbMATHGoogle Scholar
  11. DSZ10.
    Delzanno G, Sangnier A, Zavattaro G (2010) Parameterized verification of ad hoc networks. In: Concurrency theory, volume 6269 of LNCS. Springer, pp 313–327Google Scholar
  12. EJFG+10.
    Embe-Jiague M, Frappier M, Gervais F, Konopacki P, Laleau R, Milhau J, St-Denis R (2010) Model-driven engineering of functional security policies. In: International conference on enterprise information systems. SciTePress, pp 374–379Google Scholar
  13. EK00.
    Emerson EA, Kahlon V (2000) Reducing model checking of the many to the few. In: Automated deduction, volume 1831 of LNCS. Springer, pp 236–254Google Scholar
  14. ES96.
    Emerson EA, Sistla AP (1996) Symmetry and model checking. Form Methods Syst Des 9(1–2): 105–131CrossRefGoogle Scholar
  15. FFC+10.
    Frappier M, Fraikin B, Chossart R, Chane-Yack-Fa R, Ouenzar M (2010) Comparison of model checking tools for information systems. In: Formal Methods and software engineering, volume 6447 of LNCS. Springer, pp 581–596Google Scholar
  16. FGL+08.
    Frappier M, Gervais F, Laleau R, Fraikin B, St-Denis R (2008) Extending statecharts with process algebra operators. Innov Syst Softw Eng 4(3): 285–292CrossRefGoogle Scholar
  17. FGLF08.
    Frappier M, Gervais F, Laleau R, Fraikin B (2008) Algebraic state transition diagrams. Technical report, Université de Sherbrooke.
  18. Fin87.
    Finkel A (1987) A generalization of the procedure of karp and miller to well structured transition systems. In: Automata, languages and programming, volume 267 of LNCS. Springer, pp 499–508Google Scholar
  19. Fin94.
    Finkel A (1994) Decidability of the termination problem for completely specified protocols. Distrib Comput 7(3): 129–135CrossRefGoogle Scholar
  20. FS01.
    Finkel Alain, Schnoebelen Philippe (2001) Well-structured transition systems everywhere!. Theoretical Computer Science 256(1): 63–92MathSciNetCrossRefzbMATHGoogle Scholar
  21. FSD03.
    Frappier M, St-Denis R (2003) EB 3: an entity-based black-box specification method for information systems. Softw Syst Model 2(2): 134–149CrossRefGoogle Scholar
  22. Har87.
    Harel D (1987) Statecharts: a visual formalism for complex systems. Sci Comput Program 8(3): 231–274MathSciNetCrossRefzbMATHGoogle Scholar
  23. Hig52.
    Higman G (1952) Ordering by divisibility in abstract algebras. In: Proceedings of the London Mathematical Society, vol s3-2, pp 326–336Google Scholar
  24. Hoa78.
    Hoare CAR (1978) Communicating sequential processes. Commun ACM 21(8): 666–677CrossRefzbMATHGoogle Scholar
  25. HP79.
    Hopcroft J, Pansiot J-J (1979) On the reachability problem for 5-dimensional vector addition systems. Theor Comput Sci 8(2): 135–159MathSciNetCrossRefzbMATHGoogle Scholar
  26. HSBR10.
    Hanna Y, Samuelson D, Basu S, Rajan H (2010) Automating cut-off for multi-parameterized systems. In: Formal methods and software engineering, volume 6447 of LNCS. Springer, pp 338–354Google Scholar
  27. KKW10.
    Kaiser A, Kroening D, Wahl T (2010) Dynamic cutoff detection in parameterized concurrent programs. In: Computer aided verification, volume 6174 of LNCS. Springer, pp 645–659Google Scholar
  28. Kru60.
    Kruskal JB (1960) Well-quasi-ordering, the tree theorem, and Vazsonyi’s conjecture. Trans Am Math Soc 95: 210–225MathSciNetzbMATHGoogle Scholar
  29. KS14.
    König B, Stückrath J (2014) A general framework for well-structured graph transformation systems. In: Concurrency theory, volume 8704 of LNCS. Springer, pp 467–481Google Scholar
  30. McM99.
    McMillan KL (1999) Verification of infinite state systems by compositional model checking. In: Correct hardware design and verification methods, volume 1703 of LNCS. Springer, pp 219–234Google Scholar
  31. Mey09.
    Meyer R (2009) Structural Stationarity in the π-Calculus. Ph.D. thesis, Department für Informatik, Carl von Ossietzky Universität, OldenburgGoogle Scholar
  32. Mil89.
    Milner R (1989) Communication and concurrency. Prentice Hall, Upper Saddle RiverzbMATHGoogle Scholar
  33. Pet81.
    Peterson JL (1981) Petri net theory and the modeling of systems. Prentice Hall, Upper Saddle RiverzbMATHGoogle Scholar
  34. RHB97.
    Roscoe AW, Hoare CAR, Bird R (1997) The theory and practice of concurrency. Prentice Hall, Upper Saddle RiverGoogle Scholar
  35. RS10.
    Robertson N, Seymour PD (2010) Graph minors XXIII. Nash-Williams’ immersion conjecture. J Comb Theory 100(2): 181–205MathSciNetCrossRefzbMATHGoogle Scholar
  36. SK09a.
    Siirtola A, Kortelainen J (2009) Algorithmic verification with multiple and nested parameters. In: Formal methods and software engineering, volume 5885 of LNCS. Springer, pp 561–580Google Scholar
  37. SK09b.
    Siirtola A, Kortelainen J (2009) Parameterised process algebraic verification by precongruence reduction. In: Application of concurrency to system design. IEEE, pp 158–167Google Scholar
  38. SS12.
    Schmitz S, Schnoebelen P (2012) Algorithmic aspects of wqo theory. Lecture NotesGoogle Scholar
  39. VLDM16.
    Vekris D, Lang F, Dima C, Mateescu R (2016) Verification of eb3 specifications using CADP. Formal Asp Comput 28(1): 145–178MathSciNetCrossRefzbMATHGoogle Scholar

Copyright information

© British Computer Society 2018

Authors and Affiliations

  • Raphaël Chane-Yack-Fa
    • 1
  • Marc Frappier
    • 1
    Email author
  • Amel Mammar
    • 2
  • Alain Finkel
    • 3
  1. 1.GRIL, Département d’informatique, Faculté des sciencesUniversité de SherbrookeSherbrookeCanada
  2. 2.Télécom SudParis, SAMOVAR-CNRSÉvryFrance
  3. 3.LSV, CNRS & ENS Paris-SaclayUniversité Paris-SaclayParisFrance

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