Abstract
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.
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Abrial, J.-R.: The B-Book - Assigning Programs to Meanings. Cambridge University Press, Cambridge (2005)
Börger, E., Schewe, K.-D.: A behavioural theory of recursive algorithms (2019). Submitted for publication
Börger, E., Stärk, R.: Abstract State Machines. Springer, Heidelberg (2003). https://doi.org/10.1007/978-3-642-18216-7
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)
Dijkstra, E.W., Scholten, C.S.: Predicate Calculus and Program Semantics. Texts and Monographs in Computer Science. Springer, New York (1990). https://doi.org/10.1007/978-1-4612-3228-5
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). https://doi.org/10.1007/978-3-319-91271-4_14
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)
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)
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)
Gurevich, Y.: Sequential abstract state machines capture sequential algorithms. ACM Trans. Comput. Logic 1(1), 77–111 (2000)
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)
Nelson, G.: A generalization of Dijkstra’s calculus. ACM Trans. Program. Lang. Syst. 11(4), 517–561 (1989)
Schewe, K.-D.: Consistency enforcement in Entity-Relationship and object-oriented models. Data Knowl. Eng. 28(1), 121–140 (1998)
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)
Schewe, K.-D., Thalheim, B.: Towards a theory of consistency enforcement. Acta Inf. 36(2), 97–141 (1999)
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). https://doi.org/10.1007/978-3-319-98938-9_20
Thalheim, B.: Dependencies in Relational Databases. Springer, Wiesbaden (1991). https://doi.org/10.1007/978-3-663-12018-6
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Schewe, KD. (2019). Consistency Enforcement for Static First-Order Invariants in Sequential Abstract State Machines. In: Ait-Ameur, Y., Qin, S. (eds) Formal Methods and Software Engineering. ICFEM 2019. Lecture Notes in Computer Science(), vol 11852. Springer, Cham. https://doi.org/10.1007/978-3-030-32409-4_14
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DOI: https://doi.org/10.1007/978-3-030-32409-4_14
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