Consistency Enforcement for Static First-Order Invariants in Sequential Abstract State Machines

  • Klaus-Dieter ScheweEmail author
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11852)


Given a program specification P and a first-order static invariant I the problem of consistency enforcement is to determine a modified program specification \(P_I\) that is consistent with respect to I, i.e. whenever I holds in a state S it also holds in the successor states determined by \(P_I\), and at the same time only minimally deviates from P. We formalise this problem by the notion of the greatest consistent specialisation (GCS) adapting and generalising this 20 year old concept to sequential Abstract State Machines (ASMs) with emphasis on bounded parallelism. In a state satisfying I such that P is repairable the notion of consistent specialisation will require an enlargement of the update set, which defines a partial order with respect to which a GCS is defined. We show that GCSs are compositional in two respects: (1) the GCS of an ASM with a complex rule can be obtained from the GCSs of the involved assignments, and (2) the GCS with respect to a set of invariants can be built using the GCSs for the individual invariants in the set.


Consistency enforcement Static invariant Consistent specialisation Abstract State Machine Compositionality 


  1. 1.
    Abrial, J.-R.: The B-Book - Assigning Programs to Meanings. Cambridge University Press, Cambridge (2005)zbMATHGoogle Scholar
  2. 2.
    Börger, E., Schewe, K.-D.: A behavioural theory of recursive algorithms (2019). Submitted for publicationGoogle Scholar
  3. 3.
    Börger, E., Stärk, R.: Abstract State Machines. Springer, Heidelberg (2003). Scholar
  4. 4.
    Cai, C., Sun, J., Dobbie, G.: B-repair: repairing B-models using machine learning. In: 23rd International Conference on Engineering of Complex Computer Systems (ICECCS 2018), pp. 31–40. IEEE Computer Society (2018)Google Scholar
  5. 5.
    Dijkstra, E.W., Scholten, C.S.: Predicate Calculus and Program Semantics. Texts and Monographs in Computer Science. Springer, New York (1990). Scholar
  6. 6.
    Ferrarotti, F., González, S., Schewe, K.-D., Turull-Torres, J.M.: Systematic refinement of abstract state machines with higher-order logic. In: Butler, M., Raschke, A., Hoang, T.S., Reichl, K. (eds.) ABZ 2018. LNCS, vol. 10817, pp. 204–218. Springer, Cham (2018). Scholar
  7. 7.
    Ferrarotti, F., Schewe, K.-D., Tec, L., Wang, Q.: A new thesis concerning synchronised parallel computing - simplified parallel ASM thesis. Theor. Comput. Sci. 649, 25–53 (2016)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Ferrarotti, F., Schewe, K.-D., Tec, L., Wang, Q.: A complete logic for database abstract state machines. Log. J. IGPL 25(5), 700–740 (2017)Google Scholar
  9. 9.
    Ferrarotti, F., Schewe, K.-D., Tec, L., Wang, Q.: A unifying logic for non-deterministic, parallel and concurrent abstract state machines. Ann. Math. Artif. Intell. 83(3–4), 321–349 (2018)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Gurevich, Y.: Sequential abstract state machines capture sequential algorithms. ACM Trans. Comput. Logic 1(1), 77–111 (2000)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Link, S., Schewe, K.-D.: Towards an arithmetic theory of consistency enforcement based on preservation of delta-constraints. Electr. Notes Theor. Comput. Sci. 61, 64–83 (2002)CrossRefGoogle Scholar
  12. 12.
    Nelson, G.: A generalization of Dijkstra’s calculus. ACM Trans. Program. Lang. Syst. 11(4), 517–561 (1989)CrossRefGoogle Scholar
  13. 13.
    Schewe, K.-D.: Consistency enforcement in Entity-Relationship and object-oriented models. Data Knowl. Eng. 28(1), 121–140 (1998)CrossRefGoogle Scholar
  14. 14.
    Schewe, K.-D., Thalheim, B.: Limitations of rule triggering systems for integrity maintenance in the context of transition specifications. Acta Cybern. 13(3), 277–304 (1998)MathSciNetzbMATHGoogle Scholar
  15. 15.
    Schewe, K.-D., Thalheim, B.: Towards a theory of consistency enforcement. Acta Inf. 36(2), 97–141 (1999)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Schmidt, J., Krings, S., Leuschel, M.: Repair and generation of formal models using synthesis. In: Furia, C.A., Winter, K. (eds.) IFM 2018. LNCS, vol. 11023, pp. 346–366. Springer, Cham (2018). Scholar
  17. 17.
    Thalheim, B.: Dependencies in Relational Databases. Springer, Wiesbaden (1991). Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Zhejiang University, UIUC InstituteHainingChina

Personalised recommendations